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)

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=

Influence of anomalous rectifier activation on afterhyperpolarizations of neurons from cat sensorimotor cortex in vitro

1988 ◽  
Vol 59 (2) ◽  
pp. 468-481 ◽  
Author(s):  
P. C. Schwindt ◽  
W. J. Spain ◽  
W. E. Crill
Keyword(s):  
Membrane Potential ◽  
Voltage Clamp ◽  
Sensorimotor Cortex ◽  
Model Parameters ◽  
Fast Decay ◽  
Time Constants ◽  
Anomalous Rectifier ◽  
Betz Cells ◽  
K Currents

1. Large neurons from layer V of cat sensorimotor cortex (Betz cells) were studied to determine the influence of the anomalous rectifier current (IAR) on slow afterhyperpolarizations (AHPs). The neurons were examined using intracellular recording and single-microelectrode voltage clamp in an in vitro brain slice preparation. 2. A faster medium-duration AHP (mAHP) and slower AHP (sAHP) followed repetitive firing (22, 23). The amplitude of the mAHP often increased or remained constant during membrane potential hyperpolarization. The membrane potential trajectory resulting solely from IAR activation was similar to the mAHP. 3. Postrepetitive firing voltage clamp was used to measure directly slowly decaying K+ currents (IK) and IAR at different membrane potentials. IK exhibited both a fast and slow decay. The time constants of the fast decay of IK and IAR activation were similar. IAR increased with hyperpolarization or raised extracellular K+ concentration [( K+]o), whereas both the fast and slow components of IK reversed or nulled near -100 mV and behaved as pure K+ currents in response to raised [K+]o. 4. To determine the precise contribution of IK and IAR to the AHP waveform, theoretical AHPs were computed using a quantitative model based on voltage-clamp measurements. The calculated AHPs were qualitatively similar to measured AHPs. The amplitude of the mAHP showed little change with hyperpolarization because of the increasing dominance of IAR at more negative membrane potentials. The sAHP was little affected by IAR activation. 5. Several model parameters subject to biological variation among Betz cells were varied in the calculations to determine their importance in the AHP waveform. With IK parameters held constant, the amplitude and time course of the mAHP depended on resting potential, membrane time constant, the kinetics of the anomalous rectifier conductance (GAR), and the maximum value of GAR. IAR activation could result in a biphasic AHP even when the fast decay of IK was omitted from the calculations. 6. A wider variation of model parameters revealed behavior that may be relevant to other neurons. Certain values of membrane or IAR activation time constants resulted in a monophasic AHP even when the fast decay of IK was present. The decay of a biphasic AHP could reflect either the onset of IAR or the fast decay of IK, depending on the relative value of their time constants. Procedures are outlined to discriminate between these possibilities using current clamp methods.(ABSTRACT TRUNCATED AT 400 WORDS)

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)

The Action Potential in Chara coraliina II.* Two Activation-Inactivation Transients in Voltage Clamps of the Plasmalemma

1979 ◽  
Vol 6 (3) ◽  
pp. 323 ◽  
Author(s):  
M.J Beilby ◽  
H.G.L Coster
Keyword(s):  
Voltage Clamp ◽  
Outward Current ◽  
Current Transient ◽  
Equilibrium Potential ◽  
Ionic Component ◽  
Voltage Clamps ◽  
Wide Range ◽  
Ca Ions ◽  
Current Transients ◽  
Additional Current

Voltage-clamp experiments over a wide range of clamp potentials were made with cells of C. corallina using a fast voltage-clamp apparatus. Clamps of the plasmalemma potential in the range - 170 mV to - 70 mV revealed a large transient inward current which followed the usual chloride current transient hitherto described in the literature. This additional component decreased in amplitude and occurred earlier in the clamp as the clamp potentials were made more positive up to ~ -70 mV. For clamp potentials > - 50 mV, a large, prompt, outward current appeared. The additional current transients could not be observed in vacuolar potential clamp experiments, except at clamps � - 10 mV. The effects of changes in the external Cl- and Ca�+ concentrations with plasmalemma clamps at various potentials suggest that the additional transient here reported consists of a flow of Ca�+ ions and also reaffirms the identification of the other transient with a flow of Cl- ions. Reversal of the additional current transient when the clamp potential is sufficiently large (i.e. at large depolarization), places the equilibrium potential of the ionic component responsible for this transient at - 50 mV (� 20 mV). Estimates, based on this equilibrium potential, of the cytoplasmic Ca�+ concentration yield unrealistic values. Possible answers to this dilemma are discussed.

Accelerating Event-Driven Simulation of Spiking Neurons with Multiple Synaptic Time Constants

2009 ◽  
Vol 21 (4) ◽  
pp. 1068-1099 ◽  
Author(s):  
Michiel D'Haene ◽  
Benjamin Schrauwen ◽  
Jan Van Campenhout ◽  
Dirk Stroobandt
Keyword(s):  
Neuron Model ◽  
Driving Forces ◽  
Firing Time ◽  
State Variables ◽  
Neuron Models ◽  
Time Constants ◽  
Simulation Speed ◽  
Event Driven ◽  
Spiking Neuron Models ◽  
Algorithmic Techniques

The simulation of spiking neural networks (SNNs) is known to be a very time-consuming task. This limits the size of SNN that can be simulated in reasonable time or forces users to overly limit the complexity of the neuron models. This is one of the driving forces behind much of the recent research on event-driven simulation strategies. Although event-driven simulation allows precise and efficient simulation of certain spiking neuron models, it is not straightforward to generalize the technique to more complex neuron models, mostly because the firing time of these neuron models is computationally expensive to evaluate. Most solutions proposed in literature concentrate on algorithms that can solve this problem efficiently. However, these solutions do not scale well when more state variables are involved in the neuron model, which is, for example, the case when multiple synaptic time constants for each neuron are used. In this letter, we show that an exact prediction of the firing time is not required in order to guarantee exact simulation results. Several techniques are presented that try to do the least possible amount of work to predict the firing times. We propose an elegant algorithm for the simulation of leaky integrate-and-fire (LIF) neurons with an arbitrary number of (unconstrained) synaptic time constants, which is able to combine these algorithmic techniques efficiently, resulting in very high simulation speed. Moreover, our algorithm is highly independent of the complexity (i.e., number of synaptic time constants) of the underlying neuron model.

scholarly journals Extraction of Synaptic Input Properties in Vivo

2017 ◽  
Vol 29 (7) ◽  
pp. 1745-1768 ◽  
Author(s):  
Paolo Puggioni ◽  
Marta Jelitai ◽  
Ian Duguid ◽  
Mark C.W. van Rossum
Keyword(s):  
Voltage Clamp ◽  
Synaptic Input ◽  
Event Rate ◽  
Synaptic Integration ◽  
Neural Function ◽  
State Change ◽  
Input Rate ◽  
Time Constants ◽  
Synaptic Inputs

Knowledge of synaptic input is crucial for understanding synaptic integration and ultimately neural function. However, in vivo, the rates at which synaptic inputs arrive are high, so that it is typically impossible to detect single events. We show here that it is nevertheless possible to extract the properties of the events and, in particular, to extract the event rate, the synaptic time constants, and the properties of the event size distribution from in vivo voltage-clamp recordings. Applied to cerebellar interneurons, our method reveals that the synaptic input rate increases from 600 Hz during rest to 1000 Hz during locomotion, while the amplitude and shape of the synaptic events are unaffected by this state change. This method thus complements existing methods to measure neural function in vivo.

Fast and Exact Simulation Methods Applied on a Broad Range of Neuron Models

2010 ◽  
Vol 22 (6) ◽  
pp. 1468-1472 ◽  
Author(s):  
Michiel D'Haene ◽  
Benjamin Schrauwen
Keyword(s):  
Linear Models ◽  
Iteration Scheme ◽  
Integration Scheme ◽  
State Variables ◽  
Neuron Models ◽  
Time Constants ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Computation Scheme ◽  
Event Based

Recently van Elburg and van Ooyen ( 2009 ) published a generalization of the event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory currents and double exponential inhibitory synaptic currents, introduced by Carnevale and Hines. In the paper, it was shown that the constraints on the synaptic time constants imposed by the Newton-Raphson iteration scheme, can be relaxed. In this note, we show that according to the results published in D'Haene, Schrauwen, Van Campenhout, and Stroobandt ( 2009 ), a further generalization is possible, eliminating any constraint on the time constants. We also demonstrate that in fact, a wide range of linear neuron models can be efficiently simulated with this computation scheme, including neuron models mimicking complex neuronal behavior. These results can change the way complex neuronal spiking behavior is modeled: instead of highly nonlinear neuron models with few state variables, it is possible to efficiently simulate linear models with a large number of state variables.

A voltage clamp circuit for measuring rapid current transients in membranes

1976 ◽  
Vol 14 (3) ◽  
pp. 334-338 ◽  
Author(s):  
N. -E. Eriksson ◽  
J. Sandblom ◽  
J. Hägglund
Keyword(s):  
Voltage Clamp ◽  
Rapid Current ◽  
Current Transients

scholarly journals Dopaminergic and Cholinergic Modulation of Large Scale Networks in silico Using Snudda

2021 ◽  
Vol 15 ◽  
Author(s):  
Johanna Frost Nylen ◽  
Jarl Jacob Johannes Hjorth ◽  
Sten Grillner ◽  
Jeanette Hellgren Kotaleski
Keyword(s):  
Ion Channels ◽  
Large Scale ◽  
Single Cells ◽  
Critical Role ◽  
Neuron Models ◽  
Bath Application ◽  
A Cell ◽  
Large Scale Networks ◽  
Circuit Function ◽  
Large Scale Simulations

Neuromodulation is present throughout the nervous system and serves a critical role for circuit function and dynamics. The computational investigations of neuromodulation in large scale networks require supportive software platforms. Snudda is a software for the creation and simulation of large scale networks of detailed microcircuits consisting of multicompartmental neuron models. We have developed an extension to Snudda to incorporate neuromodulation in large scale simulations. The extended Snudda framework implements neuromodulation at the level of single cells incorporated into large-scale microcircuits. We also developed Neuromodcell, a software for optimizing neuromodulation in detailed multicompartmental neuron models. The software adds parameters within the models modulating the conductances of ion channels and ionotropic receptors. Bath application of neuromodulators is simulated and models which reproduce the experimentally measured effects are selected. In Snudda, we developed an extension to accommodate large scale simulations of neuromodulation. The simulator has two modes of simulation – denoted replay and adaptive. In the replay mode, transient levels of neuromodulators can be defined as a time-varying function which modulates the receptors and ion channels within the network in a cell-type specific manner. In the adaptive mode, spiking neuromodulatory neurons are connected via integrative modulating mechanisms to ion channels and receptors. Both modes of simulating neuromodulation allow for simultaneous modulation by several neuromodulators that can interact dynamically with each other. Here, we used the Neuromodcell software to simulate dopaminergic and muscarinic modulation of neurons from the striatum. We also demonstrate how to simulate different neuromodulatory states with dopamine and acetylcholine using Snudda. All software is freely available on Github, including tutorials on Neuromodcell and Snudda-neuromodulation.

scholarly journals Quantitative Analysis of Electrotonic Structure and Membrane Properties of NMDA-Activated Lamprey Spinal Neurons

1995 ◽  
Vol 7 (3) ◽  
pp. 486-506 ◽  
Author(s):  
C. R. Murphey ◽  
L. E. Moore ◽  
J. T. Buchanan
Keyword(s):  
Steady State ◽  
Voltage Clamp ◽  
Membrane Properties ◽  
Neuronal System ◽  
Cable Model ◽  
Spinal Neurons ◽  
Time Constants ◽  
Cable Properties ◽  
Wide Range ◽  
Voltage Dependent

Parameter optimization methods were used to quantitatively analyze frequency-domain-voltage-clamp data of NMDA-activated lamprey spinal neurons simultaneously over a wide range of membrane potentials. A neuronal cable model was used to explicitly take into account receptors located on the dendritic trees. The driving point membrane admittance was measured from the cell soma in response to a Fourier synthesized point voltage clamp stimulus. The data were fitted to an equivalent cable model consisting of a single lumped soma compartment coupled resistively to a series of equal dendritic compartments. The model contains voltage-dependent NMDA sensitive (INMDA), slow potassium (IK), and leakage (IL) currents. Both the passive cable properties and the voltage dependence of ion channel kinetics were estimated, including the electrotonic structure of the cell, the steady-state gating characteristics, and the time constants for particular voltage- and time-dependent ionic conductances. An alternate kinetic formulation was developed that consisted of steady-state values for the gating parameters and their time constants at half-activation values as well as slopes of these parameters at half-activation. This procedure allowed independent restrictions on the magnitude and slope of both the steady-state gating variable and its associated time constant. Quantitative estimates of the voltage-dependent membrane ion conductances and their kinetic parameters were used to solve the nonlinear equations describing dynamic responses. The model accurately predicts current clamp responses and is consistent with experimentally measured TTX-resistant NMDA-induced patterned activity. In summary, an analysis method is developed that provides a pragmatic approach to quantitatively describe a nonlinear neuronal system.

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