Estimation of the Electrical Parameters of Spinal Motoneurons Using Impedance Measurements

2004 ◽  
Vol 92 (3) ◽  
pp. 1433-1444 ◽  
Author(s):  
Mitchell G. Maltenfort ◽  
Thomas M. Hamm
Keyword(s):  
Input Resistance ◽  
Model Parameters ◽  
Phase Lag ◽  
Spinal Motoneurons ◽  
Electrical Parameters ◽  
Impedance Measurements ◽  
Dendritic Membrane ◽  
Voltage Dependent ◽  
Standard Profile ◽  
Impedance Functions

Electrical parameters of spinal motoneurons were estimated by optimizing the parameters of motoneuron models to match experimentally determined impedance functions with those of the models. The model was described by soma area, somatic and dendritic membrane resistivities, and the diameter of an equivalent dendritic cable having a standard profile. The impedance functions of motoneurons and optimized models usually differed (rms error) by <2% of input resistance. Consistent estimates for most parameters were obtained from repeated impedance determinations in individual motoneurons; estimates of dendritic resistivity were most variable. The few cells that could not be fit well had reduced impedance phase lag consistent with dendritic penetrations. Most fits were improved by inclusion of a voltage-dependent conductance GV with time constant τV. A uniformly distributed GV with τV >5 ms provided a better fit for most cells. The magnitude of this conductance decreased with depolarization. Impedance functions of other cells were adequately fit by a passive model or by a model with a somatic GV and τV <5 ms. Most of these neurons (7/8) had resting potentials positive to −60 mV. The electrotonic parameters ρ, τ, and L, estimated from model parameters, were consistent with published distributions. Most motoneuron parameters obtained in somatic shunt and sigmoidal models were well correlated, and parameters were moderately affected by changes in dendritic profile. These results demonstrate the utility and limitations of impedance measurements for estimating motoneuron parameters and suggest that voltage-dependent conductances are a substantial component of resting electrical properties.

White noise analysis of cable properties of neuroblastoma cells and lamprey central neurons

1985 ◽  
Vol 53 (3) ◽  
pp. 636-651 ◽  
Author(s):  
L. E. Moore ◽  
B. N. Christensen
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Neuroblastoma Cell ◽  
Neuroblastoma Cells ◽  
Impedance Method ◽  
Cable Properties ◽  
Dendritic Membrane ◽  
Voltage Dependent ◽  
Relaxation Time Constants ◽  
Impedance Functions

The integrative properties of two kinds of excitable cells, a cultured neuroblastoma cell and the lamprey giant interneuron, are described using a white-noise impedance method. The impedance functions were fitted with a neuron model consisting of an isopotential soma plus a single equivalent dendritic process, which contained up to 16 equal elements. The frequency-domain characteristics of both the passive and active conductances were used to estimate the dendritic-to-soma areas, the electrotonic length of an equivalent dendrite, the membrane time constant, and the relaxation time constants associated with the voltage-dependent conductances. The effect of differing degrees of synaptic input was simulated by localizing the synaptically activated conductances to the soma, a point at the end of the dendrite, or the entire dendritic membrane.

Effects of ouabain on background and voltage-dependent currents in canine colonic myocytes

1990 ◽  
Vol 259 (3) ◽  
pp. C402-C408 ◽  
Author(s):  
E. P. Burke ◽  
K. M. Sanders
Keyword(s):  
Membrane Potential ◽  
Potential Gradient ◽  
Circular Muscle ◽  
Input Resistance ◽  
Pump Current ◽  
Muscle Layer ◽  
Membrane Properties ◽  
Resting Potential ◽  
Voltage Dependent ◽  
In Cells

Previous studies have suggested that the membrane potential gradient across the circular muscle layer of the canine proximal colon is due to a gradient in the contribution of the Na(+)-K(+)-ATPase. Cells at the submucosal border generate approximately 35 mV of pump potential, whereas at the myenteric border the pump contributes very little to resting potential. Results from experiments in intact muscles in which the pump is blocked are somewhat difficult to interpret because of possible effects of pump inhibitors on membrane conductances. Therefore, we studied isolated colonic myocytes to test the effects of ouabain on passive membrane properties and voltage-dependent currents. Ouabain (10(-5) M) depolarized cells and decreased input resistance from 0.487 +/- 0.060 to 0.292 +/- 0.040 G omega. The decrease in resistance was attributed to an increase in K+ conductance. Studies were also performed to measure the ouabain-dependent current. At 37 degrees C, in cells dialyzed with 19 mM intracellular Na+ concentration [( Na+]i), ouabain caused an inward current averaging 71.06 +/- 7.49 pA, which was attributed to blockade of pump current. At 24 degrees C or in cells dialyzed with low [Na+]i (11 mM), ouabain caused little change in holding current. With the input resistance of colonic cells, pump current appears capable of generating at least 35 mV. Thus an electrogenic Na+ pump could contribute significantly to membrane potential.

scholarly journals Thermal conductivity of unsaturated clay-rocks

2010 ◽  
Vol 14 (1) ◽  
pp. 91-98 ◽  
Author(s):  
D. Jougnot ◽  
A. Revil
Keyword(s):  
Thermal Conductivity ◽  
Porous Material ◽  
Solid Phase ◽  
Model Parameters ◽  
Electrical Parameters ◽  
New Model ◽  
Unsaturated Clay ◽  
Unsaturated Porous Material ◽  
Clay Rocks ◽  
Good Agreement

Abstract. The parameters used to describe the electrical conductivity of a porous material can be used to describe also its thermal conductivity. A new relationship is developed to connect the thermal conductivity of an unsaturated porous material to the thermal conductivity of the different phases of the composite, and two electrical parameters called the first and second Archie's exponents. A good agreement is obtained between the new model and thermal conductivity measurements performed using packs of glass beads and core samples of the Callovo-Oxfordian clay-rocks at different saturations of the water phase. We showed that the three model parameters optimised to fit the new model against experimental data (namely the thermal conductivity of the solid phase and the two Archie's exponents) are consistent with independent estimates. We also observed that the anisotropy of the effective thermal conductivity of the Callovo-Oxfordian clay-rock was mainly due to the anisotropy of the thermal conductivity of the solid phase.

Voltage-Dependent Properties of Dendrites That Eliminate Location-Dependent Variability of Synaptic Input

1999 ◽  
Vol 81 (2) ◽  
pp. 535-543 ◽  
Author(s):  
Erik P. Cook ◽  
Daniel Johnston
Keyword(s):  
Synaptic Input ◽  
Outward Current ◽  
Compartment Model ◽  
Inward Current ◽  
Voltage Gated ◽  
Cable Properties ◽  
Dendritic Membrane ◽  
Voltage Dependent ◽  
Dendritic Location ◽  
Voltage Gated Channels

Voltage-dependent properties of dendrites that eliminate location-dependent variability of synaptic input. We examined the hypothesis that voltage-dependent properties of dendrites allow for the accurate transfer of synaptic information to the soma independent of synapse location. This hypothesis is motivated by experimental evidence that dendrites contain a complex array of voltage-gated channels. How these channels affect synaptic integration is unknown. One hypothesized role for dendritic voltage-gated channels is to counteract passive cable properties, rendering all synapses electrotonically equidistant from the soma. With dendrites modeled as passive cables, the effect a synapse exerts at the soma depends on dendritic location (referred to as location-dependent variability of the synaptic input). In this theoretical study we used a simplified three-compartment model of a neuron to determine the dendritic voltage-dependent properties required for accurate transfer of synaptic information to the soma independent of synapse location. A dendrite that eliminates location-dependent variability requires three components: 1) a steady-state, voltage-dependent inward current that together with the passive leak current provides a net outward current and a zero slope conductance at depolarized potentials, 2) a fast, transient, inward current that compensates for dendritic membrane capacitance, and 3) both αamino-3-hydroxy-5-methyl-4-isoxazolepropionic acid– and N-methyl-d-aspartate–like synaptic conductances that together permit synapses to behave as ideal current sources. These components are consistent with the known properties of dendrites. In addition, these results indicate that a dendrite designed to eliminate location-dependent variability also actively back-propagates somatic action potentials.

Input Resistance, Time Constants, and Spike Initiation

1998 ◽  
Author(s):  
Christof Koch
Keyword(s):  
Membrane Potential ◽  
Time Constant ◽  
Action Potentials ◽  
Input Resistance ◽  
Current Injection ◽  
Membrane Conductances ◽  
Voltage Dependent ◽  
Dc Component ◽  
Definition Of ◽  
A Current

This chapter represents somewhat of a tephnical interlude. Having introduced the reader to both simplified and more complex compartmental single neuron models, we need to revisit terrain with which we are already somewhat familiar. In the following pages we reevaluate two important concepts we defined in the first few chapters: the somatic input resistance and the neuronal time constant. For passive systems, both are simple enough variables: Rin is the change in somatic membrane potential in response to a small sustained current injection divided by the amplitude of the current injection, while τm is the slowest time constant associated with the exponential charging or discharging of the neuronal membrane in response to a current pulse or step. However, because neurons express nonstationary and nonlinear membrane conductances, the measurement and interpretation of these two variables in active structures is not as straightforward as before. Having obtained a more sophisticated understanding of these issues, we will turn toward the question of the existence of a current, voltage, or charge threshold at which a biophysical faithful model of a cell triggers action potentials. We conclude with recent work that suggests how concepts from the subthreshold domain, like the input resistance or the average membrane potential, could be extended to the case in which the cell is discharging a stream of action potentials. This chapter is mainly for the cognoscendi or for those of us that need to make sense of experimental data by comparing therp to theoretical models that usually fail to reflect reality adequately. In Sec. 3.4, we defined Kii (f) for passive cable structures as the voltage change at location i in response to a sinusoidal current injection of frequency f at the same location. Its dc component is also referred to as input resistance or Rin. Three difficulties render this definition of input resistance problematic in real cells: (1) most membranes, in particular at the soma, show voltage-dependent nonlinearities, (2) the associated ionic membrane conductances are time dependent and (3) instrumental aspects, such as the effect of the impedance of the recording electrode on Rin, add uncertainty to the measuring process.

Sodium-potassium pump inhibitors increase neuronal excitability in the rat hippocampal slice: role of a Ca2+-dependent conductance

1987 ◽  
Vol 57 (2) ◽  
pp. 496-509 ◽  
Author(s):  
M. McCarren ◽  
B. E. Alger
Keyword(s):  
Hippocampal Slice ◽  
Neuronal Excitability ◽  
Pyramidal Cells ◽  
Input Resistance ◽  
Extracellular Potassium ◽  
Gamma Aminobutyric Acid ◽  
Extracellular Potassium Concentration ◽  
Spike Threshold ◽  
Pump Activity ◽  
Voltage Dependent

We have used the rat hippocampal slice preparation as a model system for studying the epileptogenic consequences of a reduction in neuronal Na+-K+ pump activity. The cardiac glycosides (CGs) strophanthidin and dihydroouabain were used to inhibit the pump. These drugs had readily reversible effects, provided they were not applied for longer than 15-20 min. Hippocampal CA1 pyramidal cells were studied with intracellular recordings; population spike responses and changes in extracellular potassium concentration ([K+]o) were also measured in some experiments. This investigation focused on the possibility that intrinsic neuronal properties are affected by Na+-K+ pump inhibitors. The CGs altered the CA1 population response evoked by an orthodromic stimulus from a single spike to an epileptiform burst. Measurements of [K+]o showed that doses of CGs sufficient to cause bursting were associated with only minor (less than 1 mM) changes in resting [K+]o. However, the rate of K+ clearance from the extracellular space was moderately slowed, confirming that a decrease in pump activity had occurred. Intracellular recording indicated that CG application resulted in a small depolarization and apparent increase in resting input resistance of CA1 neurons. Although CGs caused a decrease in fast gamma-aminobutyric acid mediated inhibitory postsynaptic potentials (IPSPs), CGs could also enhance the latter part of the epileptiform burst induced by picrotoxin, an antagonist of these IPSPs. Since intrinsic Ca2+ conductances comprise a significant part of the burst, this suggested the possibility that Na+-K+ pump inhibitors affected an intrinsic neuronal conductance. CGs decreased the threshold for activation of Ca2+ spikes (recorded in TTX and TEA) without enhancing the spikes themselves, indicating that a voltage-dependent subthreshold conductance might be involved. The action of CGs on Ca2+ spike threshold could not be mimicked by increasing [K+]o up to 10 mM. A variety of K+ conductance antagonists, including TEA, 4-AP, Ba2+ (in zero Ca2+), and carbachol were ineffective in preventing the CG-induced threshold shift of the Ca2+ spike. The shift was also seen in the presence of a choline-substituted low Na+ saline. Enhancement of a slow inward Ca2+ current is a possible mechanism for the decrease in Ca2+ spike threshold; however, it is impossible to use the Ca2+ spike as an assay when testing the effects of blocking Ca2+ conductances. Therefore, we studied the influence of CGs on the membrane current-voltage (I-V) curve, since persistent voltage-dependent conductances appear as nonlinearities in the I-V plot obtained under current clamp.(ABSTRACT TRUNCATED AT 400 WORDS)

Nonequivalent cylinder models of neurons: interpretation of voltage transients generated by somatic current injection

1988 ◽  
Vol 60 (1) ◽  
pp. 125-148 ◽  
Author(s):  
P. K. Rose ◽  
A. Dagum
Keyword(s):  
Regional Differences ◽  
Dendritic Tree ◽  
Membrane Properties ◽  
Reliable Estimate ◽  
Voltage Response ◽  
Spinal Motoneurons ◽  
Membrane Resistivity ◽  
Voltage Dependent ◽  
Voltage Transients ◽  
Specific Membrane

1. Numerical methods were used to simulate the voltage responses to an intrasomatic current step of neuronal models that incorporated tapering dendrites, dendrites of unequal electrotonic length, nonlinear membrane properties, and regional differences in specific membrane resistivity (Rm). A "peeling" technique was used to estimate the time constants (tau 0 and tau 1) and coefficients (a0 and a1) of the first two exponential terms of the series of exponential terms whose sum represented the slope of the voltage response. 2. The electrotonic structure of models with a uniform Rm was calculated using equations derived by Rall or Johnston or Brown et al. The adequacy of these methods were tested using a wide variety of models that conformed to the equivalent cylinder approximation of Rall. Johnston's method provided the most reliable estimate of electrotonic length (L) and the ratio of the dendritic conductance to the somatic conductance (rho). However, if L exceeded 2 and rho was eight or larger, the equations derived by Johnston could frequently not be solved due to small errors in the peeled values of tau 0, tau 1, a0, and a1. Although the method suggested by Brown et al. could be applied to all models, this method invariably underestimated L and rho. These errors were particularly large for model neurons with L values of 1.5 or larger and rho values of four or larger. Estimates of L using Rall's method were only reliable if rho was large and L was two or less. 3. Changing the geometry of the dendritic tree (dendritic tapering or dendrites of unequal L) or the addition of a time- and voltage-dependent conductance designed to mimic a sag process commonly seen in spinal motoneurons caused systematic changes in tau 0, tau 1, a0, and a1. The sag process always led to an underestimate of tau 0 even after applying a correction procedure. On the other hand, the ratio, tau 0/tau 1, was not affected by the sag process or dendritic tapering.(ABSTRACT TRUNCATED AT 400 WORDS)

Excitability Increase Induced by β-Adrenergic Receptor-Mediated Activation of Hyperpolarization-Activated Cation Channels in Rat Cerebellar Basket Cells

2000 ◽  
Vol 84 (4) ◽  
pp. 2026-2034 ◽  
Author(s):  
Fumihito Saitow ◽  
Shiro Konishi
Keyword(s):  
Preceding Paper ◽  
Input Resistance ◽  
Ionic Currents ◽  
Synaptic Activity ◽  
Basket Cells ◽  
Camp Analogue ◽  
Voltage Dependent ◽  
Current Clamp Mode ◽  
Old Rats ◽  
Whole Cell Recordings

In the preceding paper, we showed that norepinephrine (NE) enhances the spontaneous spike firings in cerebellar interneurons, basket cells (BCs), resulting in an increase in the frequency of BC-spike-triggered inhibitory postsynaptic currents (IPSCs) in Purkinje cells (PCs), and that the effects of NE on GABAergic BCs are mediated by β2-adrenergic receptors. This study aimed to further examine the ionic mechanism underlying the β-adrenoceptor-mediated facilitation of GABAergic transmission at the BC-PC synapses. Using cerebellar slices obtained from 15- to 21-day-old rats and whole cell recordings, we investigated ionic currents in the BCs and the effects of the β-agonist isoproterenol (ISP) as well as forskolin on the BC excitability. Hyperpolarizing voltage steps from a holding potential of −50 mV elicited a hyperpolarization-activated inward current, I h, in the BC. This current exhibited voltage-dependent activation that was accelerated by strong hyperpolarization, displaying two time constants, 84 ± 6 and 310 ± 40 ms, at −100 mV, and was inhibited by 20 μM ZD7288. ISP and forskolin, both at 20 μM, enhanced I h by shifting the activation curve by 5.9 and 9.3 mV toward positive voltages, respectively. Under the current-clamp mode, ISP produced a depolarization of 7 ± 3 mV in BCs and reduced their input resistance to 74 ± 6%. ISP and a cAMP analogue, Rp-cAMP-S, increased the frequency of spontaneous spikes recorded from BCs using the cell-attached mode. The I h inhibitor ZD7288 decreased the BC spike frequency and abolished the ISP-induced increase in spike discharges. The results suggest that NE depolarizes the BCs through β-adrenoceptor-mediated cAMP formation linking it to activation of I h, which is, at least in part, involved in noradrenergic afferent-mediated facilitation of GABAergic synaptic activity at BC-PC connections in the rat cerebellum.

Estimating the electrotonic structure of neurons with compartmental models

1992 ◽  
Vol 68 (4) ◽  
pp. 1438-1452 ◽  
Author(s):  
W. R. Holmes ◽  
W. Rall
Keyword(s):  
Input Resistance ◽  
Morphological Data ◽  
Unknown Parameters ◽  
Membrane Area ◽  
Time Constants ◽  
Fitting Procedure ◽  
Dendritic Membrane ◽  
Membrane Resistivity ◽  
Soma Membrane ◽  
Current Transients

1. A procedure based on compartmental modeling called the "constrained inverse computation" was developed for estimating the electrotonic structure of neurons. With the constrained inverse computation, a set of N electrotonic parameters are estimated iteratively with use of a Newton-Raphson algorithm given values of N parameters that can be measured or estimated from experimental data. 2. The constrained inverse computation is illustrated by several applications to the basic example of a neuron represented as one cylinder coupled to a soma. The number of unknown parameters estimated was different (ranging from 2 to 6) when different sets of constraints were chosen. The unknowns were chosen from the following: dendritic membrane resistivity Rmd, soma membrane resistivity Rms, intracellular resistivity Ri, membrane capacity Cm, dendritic membrane area AD, soma membrane area As, electrotonic length L, and resistivity-free length, rfl (rfl = 2l/d1/2 where l and d are length and diameter of the cylinder). The values of the unknown parameters were estimated from the values of an equal number of known parameters, which were chosen from the following: the time constants and coefficients of a voltage transient tau 0, tau 1, ..., C0, C1, ..., voltage-clamp time constants tau vc1, tau vc2, ..., and input resistance RN. Note that initially, morphological data were treated as unknown, rather than known. 3. When complete morphology was not known, parameters from voltage and current transients, combined with the input resistance were not sufficient to completely specify the electrotonic structure of the neuron. For a neuron represented as a cylinder coupled to a soma, there were an infinite number of combinations of Rmd, Rms, Ri, Cm, AS, AD, and L that could be fitted to the same voltage and current transients and input resistance. 4. One reason for the nonuniqueness when complete morphology was not specified is that the Ri estimate is intrinsically bound to the morphology. Ri enters the inverse computation only in the calculation of the electrotonic length of a compartment. The electrotonic length of a compartment is l[4 Ri/(dRmd)]1/2, where l and d are the length and diameter of the compartment. Without complete morphology, the inverse computation cannot distinguish between a change in d or l and a change in Ri. Even when morphology is known, the accuracy of the Ri estimate obtained by any fitting procedure is affected by systematic errors in length and diameter measurements (i.e., tissue shrinkage); the Ri estimate is inversely proportional to the length measurement and proportional to the square root of the diameter measurement.(ABSTRACT TRUNCATED AT 400 WORDS)

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