Voltage-Dependent Events in the Dendritic Tree

1998 ◽  
Author(s):  
Christof Koch
Keyword(s):  
Dendritic Tree ◽  
Biophysical Modeling ◽  
Functional Roles ◽  
Initiation Zone ◽  
Cable Theory ◽  
Membrane Conductances ◽  
Cable Properties ◽  
Voltage Dependent ◽  
The Face ◽  
Spike Initiation

So far, we worked under the convenient fiction that active, voltage-dependent membrane conductances are confined to the spike initiation zone at or close to the cell body and that the dendritic tree is essentially passive. Under the influence of one-dimensional passive cable theory, as refined by Rail and his school (Chaps. 2 and 3), the passive model of dendritic integration of synaptic inputs has become dominant and is taught in all the textbooks. Paradoxically, from the earliest days of intracellular recordings from the fat dendrites of spinal cord motoneurons with the aid of glass microelectrodes, active dendritic responses had been witnessed (Brock, Coombs, and Eccles, 1952; Eccles, Libet, and Young, 1958). Today, there exists overwhelming evidence for a host of voltage-dependent sodium and calcium-conductances in the dendritic tree. In the following section we summarize the experimental evidence and discuss current biophysical modeling efforts focusing on the question of the existence and genesis of fast all-or-none electrical events in the dendrites. We then turn toward possible functional roles of active dendritic processing. One word of advice. It has been argued that linear cable theory as applied to dendrites and taught in the first chapters of this book is irrelevant in the face of all this evidence for active processing and can be relegated to the dustbin. However, this would be a mistake. Under many physiological conditions these nonlinearities will not be relevant. Even if they are, the resistive and capacitive cable properties of the dendrites profoundly influence the initiation and propagation of dendritic action potentials and other active phenomena. Thus, for a complete understanding of the events in active dendritic trees we need to be thoroughly versed in cable theory. The issue of dendritic all-or-none electrical events must be seen as separate from the broader question of the existence and nature of active, that is, voltage-dependent, membrane conductances in the dendritic tree.

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.

Synaptic Interactions in a Passive Dendritic Tree

1998 ◽  
Author(s):  
Christof Koch
Keyword(s):  
Nervous System ◽  
Dendritic Tree ◽  
Extreme Case ◽  
Pyramidal Cells ◽  
Inhibitory Synapses ◽  
Dendritic Trees ◽  
Central Processing ◽  
Voltage Dependent ◽  
Dendritic Spikes ◽  
Spatial Positioning

Nerve cells are the targets of many thousands of excitatory and inhibitory synapses. An extreme case are the Purkinje cells in the primate cerebellum, which receive between one and two hundred thousand synapses onto dendritic spines from an equal number of parallel fibers (Braitenberg and Atwood, 1958; Llinas and Walton, 1998). In fact, this structure has a crystalline-like quality to it, with each parallel fiber making exactly one synapse onto a spine of a Purkinje cell. For neocortical pyramidal cells, the total number of afferent synapses is about an order of magnitude lower (Larkman, 1991). These numbers need to be compared against the connectivity in the central processing unit (CPU) of modern computers, where the gate of a typical transistor usually receives input from one, two, or three other transistors or connects to one, two, or three other transistor gates. The large number of synapses converging onto a single cell provide the nervous system with a rich substratum for implementing a very large class of linear and nonlinear neuronal operations. As we discussed in the introductory chapter, it is only these latter ones, such as multiplication or a threshold operation, which are responsible for “computing” in the nontrivial sense of information processing. It therefore becomes crucial to study the nature of the interaction among two or more synaptic inputs located in the dendritic tree. Here, we restrict ourselves to passive dendritic trees, that is, to dendrites that do not contain voltage-dependent membrane conductances. While such an assumption seemed reasonable 20 or even 10 years ago, we now know that the dendritic trees of many, if not most, cells contain significant nonlinearities, including the ability to generate fast or slow all-or-none electrical events, so-called dendritic spikes. Indeed, truly passive dendrites may be the exception rather than the rule in the nervous In Sec. 1.5, we studied this interaction for the membrane patch model. With the addition of the dendritic tree, the nervous system has many more degrees of freedom to make use of, and the strength of the interaction depends on the relative spatial positioning, as we will see now. That this can be put to good use by the nervous system is shown by the following experimental observation and simple model.

Synaptic integration in an excitable dendritic tree

1993 ◽  
Vol 70 (3) ◽  
pp. 1086-1101 ◽  
Author(s):  
B. W. Mel
Keyword(s):  
Pyramidal Cell ◽  
Neuronal Response ◽  
Dendritic Tree ◽  
Pattern Discrimination ◽  
Synaptic Activity ◽  
Visual Neurons ◽  
Voltage Dependent ◽  
Sum Of Products ◽  
Very High ◽  
Synaptic Drive

1. Compartmental modeling experiments were carried out in an anatomically characterized neocortical pyramidal cell to study the integrative behavior of a complex dendritic tree containing active membrane mechanisms. Building on a previously presented hypothesis, this work provides further support for a novel principle of dendritic information processing that could underlie a capacity for nonlinear pattern discrimination and/or sensory processing within the dendritic trees of individual nerve cells. 2. It was previously demonstrated that when excitatory synaptic input to a pyramidal cell is dominated by voltage-dependent N-methyl-D-aspartate (NMDA)-type channels, the cell responds more strongly when synaptic drive is concentrated within several dendritic regions than when it is delivered diffusely across the dendritic arbor. This effect, called dendritic "cluster sensitivity," persisted under wide-ranging parameter variations and directly implicated the spatial ordering of afferent synaptic connections onto the dendritic tree as an important determinant of neuronal response selectivity. 3. In this work, the sensitivity of neocortical dendrites to spatially clustered synaptic drive has been further studied with fast sodium and slow calcium spiking mechanisms present in the dendritic membrane. Several spatial distributions of the dendritic spiking mechanisms were tested with and without NMDA synapses. Results of numerous simulations reveal that dendritic cluster sensitivity is a highly robust phenomenon in dendrites containing a sufficiency of excitatory membrane mechanisms and is only weakly dependent on their detailed spatial distribution, peak conductances, or kinetics. Factors that either work against or make irrelevant the dendritic cluster sensitivity effect include 1) very high-resistance spine necks, 2) very large synaptic conductances, 3) very high baseline levels of synaptic activity, and 4) large fluctuations in level of synaptic activity on short time scales. 4. The functional significance of dendritic cluster sensitivity has been previously discussed in the context of associative learning and memory. Here it is demonstrated that the dendritic tree of a cluster-sensitive neuron implements an approximative spatial correlation, or sum of products operation, such as that which could underlie nonlinear disparity tuning in binocular visual neurons.

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)

scholarly journals Location and Plasticity of the Sodium Spike Initiation Zone in Nociceptive Terminals In Vivo

Neuron ◽  
2019 ◽  
Vol 102 (4) ◽  
pp. 801-812.e5 ◽  
Author(s):  
Robert H. Goldstein ◽  
Omer Barkai ◽  
Almudena Íñigo-Portugués ◽  
Ben Katz ◽  
Shaya Lev ◽  
...  
Keyword(s):  
Initiation Zone ◽  
Spike Initiation

Passive current flow and morphology in the terminal arborizations of the posterior pituitary

1993 ◽  
Vol 69 (3) ◽  
pp. 692-702 ◽  
Author(s):  
M. B. Jackson
Keyword(s):  
Action Potentials ◽  
Current Flow ◽  
Membrane Properties ◽  
Nerve Terminals ◽  
Posterior Pituitary ◽  
Cable Theory ◽  
Cable Properties ◽  
Length Constant ◽  
Passive Current ◽  
Current Transients

1. Patch-clamp techniques were used to study the morphology and electrotonic properties of the terminal arborizations of the posterior pituitary. 2. Neurobiotin-labeling experiments revealed axons and swellings connected to the structure that was patch clamped. The large swellings were en passant and situated along axons in a topological arrangement identical to that of the small varicosities. Axons had many varicosities and few branches, reflecting a predominant architectural motif of beads on a string rather than berries on a bush. 3. Cable theory was used to analyze passive current transients produced by voltage steps under whole-cell clamp. Most charging transients were not consistent with an equivalent cylinder representation as posited by the Rall model for a motoneuron. A few charging transients were consistent with the Rall model and provided estimates for basic membrane and cable properties. 4. Some of the charging transients that violated predictions of the Rall model were consistent with an alternative model, in which the patch-clamped swelling was assumed to be coupled to another swelling by a segment of axon. This model was called the Dumbbell model, and it, together with the neurobiotin-labeling experiments, indicated that a significant number of large swellings were less than one length constant away from another large swelling. 5. Large swellings can have diameters approximately 30 times larger than the diameters of the connecting axons. These swellings lie along the axon such that action potentials must propagate through them to spread excitation through the entire terminal arborization. These large swellings could be sites where action-potential propagation is more likely to fail. 6. The information presented here about neurohypophysial nerve terminals should be useful in further investigations of how terminal arborization geometry and membrane properties influence neurosecretion and synaptic transmission.

scholarly journals Optical measurement of conduction in single demyelinated axons.

1990 ◽  
Vol 95 (5) ◽  
pp. 867-889 ◽  
Author(s):  
P Shrager ◽  
C T Rubinstein
Keyword(s):  
Schwann Cells ◽  
Action Potentials ◽  
Spontaneous Recovery ◽  
Demyelinating Disease ◽  
Optical Measurement ◽  
Recovery Of Function ◽  
Na Channels ◽  
Cable Properties ◽  
Probability Of Success ◽  
Voltage Dependent

Demyelination was initiated in Xenopus sciatic nerves by an intraneural injection of lysolecithin over a 2-3-mm region. During the next week macrophages and Schwann cells removed all remaining damaged myelin by phagocytosis. Proliferating Schwann cells then began to remyelinate the axons, with the first few lamellae appearing 13 d after surgery. Action potentials were recorded optically through the use of a potential-sensitive dye. Signals could be detected both at normal nodes of Ranvier and within demyelinated segments. Before remyelination, conduction through the lesion occurred in only a small fraction of the fibers. However, in these particular cases we could demonstrate continuous (nonsaltatory) conduction at very low velocities over long (greater than one internode) lengths of demyelinated axons. We have previously found through loose patch clamp experiments that the internodal axolemma contains voltage-dependent Na+ channels at a density approximately 4% of that at the nodes. These channels alone, however, are insufficient for successful conduction past the transition point between myelinated and demyelinated regions. Small improvements in the passive cable properties of the axon, adequate for propagation at this site, can be realized through the close apposition of macrophages and Schwann cells. As the initial lamellae of myelin appear, the probability of success at the transition zone increases rapidly, though the conduction velocity through the demyelinated segment is not appreciably changed. A detailed computational model is used to test the relative roles of the internodal Na+ channels and the new extracellular layer. The results suggest a possible mechanism that may contribute to the spontaneous recovery of function often seen in demyelinating disease.

scholarly journals Covariation of axon initial segment location and dendritic tree normalizes the somatic action potential

2016 ◽  
Vol 113 (51) ◽  
pp. 14841-14846 ◽  
Author(s):  
Mustafa S. Hamada ◽  
Sarah Goethals ◽  
Sharon I. de Vries ◽  
Romain Brette ◽  
Maarten H. P. Kole
Keyword(s):  
Action Potential ◽  
Initial Segment ◽  
Pyramidal Neurons ◽  
Dendritic Tree ◽  
Apical Dendrite ◽  
Axial Current ◽  
Axon Initial Segment ◽  
Output Code ◽  
The Face ◽  
Dendritic Complexity

In mammalian neurons, the axon initial segment (AIS) electrically connects the somatodendritic compartment with the axon and converts the incoming synaptic voltage changes into a temporally precise action potential (AP) output code. Although axons often emanate directly from the soma, they may also originate more distally from a dendrite, the implications of which are not well-understood. Here, we show that one-third of the thick-tufted layer 5 pyramidal neurons have an axon originating from a dendrite and are characterized by a reduced dendritic complexity and thinner main apical dendrite. Unexpectedly, the rising phase of somatic APs is electrically indistinguishable between neurons with a somatic or a dendritic axon origin. Cable analysis of the neurons indicated that the axonal axial current is inversely proportional to the AIS distance, denoting the path length between the soma and the start of the AIS, and to produce invariant somatic APs, it must scale with the local somatodendritic capacitance. In agreement, AIS distance inversely correlates with the apical dendrite diameter, and model simulations confirmed that the covariation suffices to normalize the somatic AP waveform. Therefore, in pyramidal neurons, the AIS location is finely tuned with the somatodendritic capacitive load, serving as a homeostatic regulation of the somatic AP in the face of diverse neuronal morphologies.

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