Intrinsic and extrinsic determinants of ion channel localization in neurons

Neurons are an extremely diverse group of excitable cells with a wide variety of morphologies including complex dendritic trees and very long axons. The electrical properties of neurons depend not only on the types of ion channels and receptors expressed, but also on where these channels are located in the cell. Two extreme examples that illustrate the subcellular polarized nature of neurons and the tight regulation of ion channel localization can be seen at the axon initial segment and the node of Ranvier. The axon initial segment is important for initiation of action potentials in the axon, whereas the node of Ranvier is required for the rapid, faithful and efficient propagation of action potentials along the axon. Given the similarity of their functions it is not surprising that nearly every protein component of the axon initial segment is also found at the node. However, there is one very important difference between these two sites: nodes require extrinsic, glial-derived factors in order to form, whereas the axon initial segment is intrinsically determined by the neuron. This mini-review discusses recent results that have begun to clarify the intrinsic and extrinsic mechanisms underlying formation of nodes and axon initial segments, and poses several important unanswered questions regarding their unique mechanisms of formation.     

Transient Response in a Dendritic Neuron Model for Current Injected at One Branch

Mathematical expressions are obtained for the response function corresponding to an instantaneous pulse of current injected to a single dendritic branch in a branched dendritic neuron model. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. The response function when used in a convolution formula enables one to compute the voltage transient at any specified point in the dendritic tree for an arbitrary current injection at a given input location. A particular numerical example, for a brief current injection at a branch terminal, illustrates the attenuation and delay characteristics of the depolarization peak as it spreads throughout the neuron model. In contrast to the severe attenuation of voltage transients from branch input sites to the soma, the fraction of total input charge actually delivered to the soma and other trees is calculated to be about one-half. This fraction is independent of the input time course. Other numerical examples, which compare a branch terminal input site with a soma input site, demonstrate that, for a given transient current injection, the peak depolarization is not proportional to the input resistance at the injection site and, for a given synaptic conductance transient, the effective synaptic driving potential can be significantly reduced, resulting in less synaptic current flow and charge, for a branch input site. Also, for the synaptic case, the two inputs are compared on the basis of the excitatory post-synaptic potential (EPSP) seen at the soma and the total charge delivered to the soma.     

Branch Input Resistance and Steady Attenuation for Input to One Branch of a Dendritic Neuron Model

Mathematical solutions and numerical illustrations are presented for the steady-state distribution of membrane potential in an extensively branched neuron model, when steady electric current is injected into only one dendritic branch. Explicit expressions are obtained for input resistance at the branch input site and for voltage attenuation from the input site to the soma; expressions for AC steady-state input impedance and attenuation are also presented. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. Numerical examples illustrate how branch input resistance and steady attenuation depend upon the following: the number of dendritic trees, the orders of dendritic branching, the electrotonic length of the dendritic trees, the location of the dendritic input site, and the input resistance at the soma. The application to cat spinal motoneurons, and to other neuron types, is discussed. The effect of a large dendritic input resistance upon the amount of local membrane depolarization at the synaptic site, and upon the amount of depolarization reaching the soma, is illustrated and discussed; simple proportionality with input resistance does not hold, in general. Also, branch input resistance is shown to exceed the input resistance at the soma by an amount that is always less than the sum of core resistances along the path from the input site to the soma.     

Variability of adaptational properties of an excitable neuron membrane

This investigation was made on a preparation of stretch receptors of molting crayfish. We made intracellular recordings of potentials from the soma of a slowly-adapting neuron, and extracellular recordings from the nerve trunk. After strychnine had been added to the physiological solution surrounding the preparation, additional rhythmic activity was recorded from the nerve trunk, with corresponding depolarizational oscillations in the membrane potential of the soma of the slowly-adapting neuron. The additional rhythmic activity had a competitive relationship to the action potentials lying along the axon of the slowly-adapting neuron, the rhythm frequency increasing as the prolonged action potentials arose in the soma of that neuron. The depolarizational oscillations in the soma did not change sign as its membrane potential decreased. Analysis of the above phenomenon led to the conclusion that within the axon membrane of a slowly-adapting neuron there appears a section that spontaneously generates rhythmic action potentials. The results of the investigation indicate that there may be wide variations in the adaptational properties of the neuron membrane.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 1, No. 3, pp. 309–314, November–December, 1969.     

Solutions for transients in arbitrarily branching cables: II. Voltage clamp theory

Analytical solutions are derived for arbitrarily branching passive neurone models with a soma and somatic shunt, for synaptic inputs and somatic voltage commands, for both perfect and imperfect somatic voltage clamp. The solutions are infinite exponential series. Perfect clamp decouples different dendritic trees at the soma: each exponential component exists only in one tree; its time constant is independent of stimulating and recording position within the tree; its amplitude is the product of a factor constant over that entire tree and factors dependent on stimulating and recording positions. Imperfect clamp to zero is mathematically equivalent to voltage recording with a shunt. As the series resistance increases, different dendritic trees become more strongly coupled. A number of interesting response symmetries are evident. The solutions reveal parameter dependencies, including an insensitivity of the early parts of the responses to specific membrane resistivity and somatic shunt, and an approximately linear dependence of the slower time constants on series resistance, for small series resistances. The solutions are illustrated using a “cartoon” representation of a CA1 pyramidal cell and a two-cylinder + soma model.     

Firing properties of the soma and axon of the abdominal stretch receptor neurons in the crayfish (Astacus leptodactylus)

Action potentials (APs) and impulse responses in the soma and axon of the rapidly and slowly adapting (SA) abdominal stretch receptor neurons of the crayfish (Astacus leptodactylus) were recorded with single microelectrode current-clamp technique. Impulse frequency response to constant current injection was almost constant in the SA neuron while the response decayed completely in the rapidly adapting (RA) neuron. Mean impulse frequency responses to current stimulations were similar in the receptor neuron pairs. In the RA neuron additional current steps evoked additional impulses while a sudden drop in the current amplitude caused adaptation. Impulse duration was dependent on the rate of rise when current ramps were used. Adaptation was facilitated when calculated receptor current was used. Exposing the neuron to 3 mmol/l TEA or scorpion venom resulted in partly elongated impulse responses. SA neuron could continuously convert the current input into impulse frequency irrespective of previous stimulation conditions. Exposing the SA neuron to 3 mmol/l TEA or 1 mmol/l Lidocaine reduced impulse duration to large current stimulations. The SA neuron fired spontaneously if it was exposed to 5-10 mmol/l Lidocaine or 10(-2) mg/ml Leiurus quinquestriatus venom. The action potential (AP) amplitudes in the RA soma, RA axon, SA soma, and SA axon were significantly different between components of all pairs. Duration of the AP in the axon of the RA neuron was significantly shorter than those in the RA soma, SA soma, and SA axon. Diameter of the RA axon was larger than that of the SA axon. Non-adapting impulse responses were promptly observed only in the SA axons. The results indicate that the RA neuron is a sort of rate receptor transducing the rapid length changes in the receptor muscle while the SA neuron is capable of transducing the maintained length changes in the receptor muscle. The differences in firing properties mainly originate from the differences in the active and passive properties of the receptor neurons.     

Electrotonic measurements by electric field-induced polarization in neurons: theory and experimental estimation

We present a theory for estimation of the dendritic electrotonic length constant and the membrane time constant from the transmembrane potential (TMP) induced by an applied electric field. The theory is adapted to morphologically defined neurons with homogeneous passive electric properties. Frequency characteristics and transients at the onset and offset of the DC field are considered. Two relations are useful for estimating the electrotonic parameters: 1) steady-state polarization versus the dendritic electrotonic length constant; 2) membrane time constant versus length constant. These relations are monotonic and may provide a unique estimate of the electrotonic parameters for 3D-reconstructed neurons. Equivalent tip-to-tip electrotonic length of the dendritic tree was estimated by measuring the equalization time of the field-induced TMP. For 11 turtle spinal motoneurons, the electrotonic length from tip to tip of the dendrites was in the range of 1-2.5 lambda, whereas classical estimation using injection of current pulses gave an average dendrite length of 0.9-1.1 lambda. For seven ventral horn interneurons, the estimates were 0.7-2.6 lambda and 0.6-0.9 lambda, respectively. The measurements of the field-induced polarization promise to be a useful addition to the conventional methods using microelectrode stimulation.     

The spatial pattern of light determines the kinetics and modulates backpropagation of optogenetic action potentials

Optogenetics offers an unprecedented ability to spatially target neuronal stimulations. This study investigated via simulation, for the first time, how the spatial pattern of excitation affects the response of channelrhodopsin-2 (ChR2) expressing neurons. First we described a methodology for modeling ChR2 in the NEURON simulation platform. Then, we compared four most commonly considered illumination strategies (somatic, dendritic, axonal and whole cell) in a paradigmatic model of a cortical layer V pyramidal cell. We show that the spatial pattern of illumination has an important impact on the efficiency of stimulation and the kinetics of the spiking output. Whole cell illumination synchronizes the depolarization of the dendritic tree and the soma and evokes spiking characteristics with a distinct pattern including an increased bursting rate and enhanced back propagation of action potentials (bAPs). This type of illumination is the most efficient as a given irradiance threshold was achievable with only 6 % of ChR2 density needed in the case of somatic illumination. Targeting only the axon initial segment requires a high ChR2 density to achieve a given threshold irradiance and a prolonged illumination does not yield sustained spiking. We also show that patterned illumination can be used to modulate the bAPs and hence spatially modulate the direction and amplitude of spike time dependent plasticity protocols. We further found the irradiance threshold to increase in proportion to the demyelination level of an axon, suggesting that measurements of the irradiance threshold (for example relative to the soma) could be used to remotely probe a loss of neural myelin sheath, which is a hallmark of several neurodegenerative diseases.     

Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.     

Synaptic potentials and transfer functions of lamprey spinal neurons

1. Electrotonic and chemical synaptic potentials were measured as a function of frequency of presynaptic action potentials. Over the frequency range from 0.02 to 10 Hz, the electrotonic synaptic potential was constant, while the chemical synaptic potential decreased in magnitude. Above 10 Hz, both synaptic events decreased in magnitude consistent with filtering by the dendritic structures. 2. Electrotonic synaptic transfer functions from 0.5 to 100 Hz were measured for the I1 reticulospinal Müller axon to spinal neuron electrotonic synaptic junction of the lamprey spinal cord using paired recordings from the pre-synaptic terminals and the post-synaptic neurons. In addition to this two-point synaptic transfer function, individual single point impedance functions of both the post-synaptic soma and the pre-synaptic axon terminal were measured. 3. The measured functions were interpreted with a computational model based on a three dimensional reconstruction of a Lucifer yellow filled motoneuron. Simulations of the model for a synaptic location of the I1 synapse were consistent with the measured synaptic transfer functions. 4. Synaptic potentials were simulated for inputs on dendrites near the I1 axon as well as distal dendritic regions. The high frequency filtering increased as the synaptic location was moved from the soma to the periphery, but the potential response on distal dendrites was larger than would have been predicted from the end of the equivalent cylinder of a Rall model that was used to fit soma impedance functions. 5. Electrotonic post-synaptic potentials were enhanced by the activation of a TTX-sensitive negative conductance.(ABSTRACT TRUNCATED AT 250 WORDS)     

Axons of sacral preganglionic neurons in the cat: I. Origin,initial segment,and myelination

Parasympathetic preganglionic neurons in the cat sacral spinal cord innervate intraspinal neurons and pelvic target organs. Retrograde tracing studies have revealed little of the morphology of their axons including their origin, initial segments, or their myelin, due to methodological limitations. Intracellular labeling of single neurons with neurobiotin or HRP has overcome these problems. Axons were studied in 24 preganglionic neurons. In 21 neurons the axon originated as a branch of a dendrite, without a detectable axon hillock, at distances from the soma ranging from 10 to 110 μm (average 34.1 μm ). In 3 neurons the axon was derived from the soma. Initial segments, present in all cells, ranged from 15 to 40 μm (average 26.8 μm). Nearly all axons followed the initial segment with unmyelinated segments that varied between 59 to 630 μm, followed by myelin and nodes of Ranvier. Internodal distances were variable and relatively short (average 93 μm). Axonal diameters measured over the intraspinal course in 18 axons averaged 1.3 μm (range 0.6–2.4 μm) and were relatively constant compared with other neurons. Spine-like protrusions were observed on the initial segments of 12 cells. Axon collaterals originated from unmyelinated sections and nodes of Ranvier. Antidromic action potentials showing initial segment, soma-dendritic inflections, did not differentiate between soma-derived and dendrite-derived axons. The data suggest that axons originating from a dendrite are the normal structure of preganglionic neurons in the lateral sacral parasympathetic nucleus. It is proposed that the particular structure of these axons may be part of a timing mechanism that coordinates preganglionic neurons with other spinal neurons involved in target organ reflexes.     

Excitation of central nervous system neurons by nonuniform electric fields.

The goal of this study was to determine which neural elements are excited by microstimulation of the central nervous system. A cable model of a neuron including an axon, initial segment, axon hillock, soma, and simplified dendritic tree was used to study excitation with an extracellular point source electrode. The model reproduced a wide range of experimentally documented extracellular excitation patterns. The site of action potential initiation (API) was a function of the electrode position, stimulus duration, and stimulus polarity. The axon or initial segment was always the site of API at threshold. When the electrode was positioned near the cell body, the site of excitation was dependent on the stimulus amplitude. With the electrode in close proximity to the neuron, short-duration cathodic pulses produced lower thresholds with the electrode positioned over the axon than over the cell body, and long-duration stimuli produced opposite relative thresholds. This result was robust to alterations in either the maximum conductances or the intracellular resistivities of the model. The site of maximum depolarization was not always an accurate predictor of the site of API, and the temporal evolution of the changes in membrane potential played a strong role in determining the site of excitation.     

Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.     

Transient response in a somatic shunt cable model for synaptic input activated at the terminal

Rall's neuron model is extended by including a non-uniform time constant together with synaptic input modeled as a square step of conductance. An analytic solution (in series form) for the electrotonic potential is obtained. The major conclusion reached is that a lower somatic time constant attenuates the amplitude of the potential at the soma, brought about by the activation of a synapse located at the distal end of the dendritic cable in an initially polarized neuron.     

Serotonin-immunoreactive neurons in the antennal sensory system of the brain in the carpenter ant, Camponotus japonicus

Social Hymenoptera such as ants or honeybees are known for their extensive behavioral repertories and plasticity. Neurons containing biogenic amines appear to play a major role in controlling behavioral plasticity in these insects. Here we describe the morphology of prominent serotonin-immunoreactive neurons of the antennal sensory system in the brain of an ant, Camponotus japonicus. Immunoreactive fibers were distributed throughout the brain and the subesophageal ganglion (SOG). The complete profile of a calycal input neuron was identified. The soma and dendritic elements are contralaterally located in the lateral protocerebrum. The neuron supplies varicose axon terminals in the lip regions of the calyces of the mushroom body, axon collaterals in the basal ring but not in the collar region, and other axon terminals ipsilaterally in the lateral protocerebrum. A giant neuron innervating the antennal lobe has varicose axon terminals in most of 300 glomeruli in the ventral region of the antennal lobe (AL) and a thick neurite that spans the entire SOG and continues towards the thoracic ganglia. However, neither a soma nor a dendritic element of this neuron was found in the brain or the SOG. A deutocerebral projection neuron has a soma in the lateral cell-body group of the AL, neuronal branches at most of the 12 glomeruli in the dorsocentral region of the ipsilateral AL, and varicose terminal arborizations in both hemispheres of the protocerebrum. Based on the present results, tentative subdivisions in neuropils related to the antennal sensory system of the ant brain are discussed.     

Dendritic analysis of lobster stretch receptor neurons: Electrotonic properties with single and distributed inputs

Using steady-state cable analysis as derived by Rall, electrotonic properties of the dendritic trees of the tonic stretch receptor neuron of the spiny lobster, Panulirus interruptus,have been examined. By directly measuring the somatic input resistance and by visualizing the dendritic trees of this neuron by backfilling the axon with cobalt, the electrotonic properties of the dendritic trees have been derived. The calculated membrane resistivity is 800-3600 -cm ². Voltage and current transfer functions were calculated for (a) single dendritic tips the size observed in the cobalt preparations and (b) for processes 2 µm or smaller, as observed in electron microscopy. Current transfer to the soma was high in both cases (greater than 80%). Voltage transfer was 22% for large and 4% for small dendrites. When a more natural simultaneous conductance change at the tips of all major dendrites was modeled, voltage transfer was 84% and current transfer 56%. But the dynamic range of the cell (rheobase to saturation) is well-predicted by varying the simultaneous inputs, not by scaling up a single input, thus illustrating that convenient indices of electrotonic properties may not prove useful in appreciating the integrative properties of a neuron.     

Mechanisms of magnetic stimulation of central nervous system neurons

Transcranial magnetic stimulation (TMS) is a stimulation method in which a magnetic coil generates a magnetic field in an area of interest in the brain. This magnetic field induces an electric field that modulates neuronal activity. The spatial distribution of the induced electric field is determined by the geometry and location of the coil relative to the brain. Although TMS has been used for several decades, the biophysical basis underlying the stimulation of neurons in the central nervous system (CNS) is still unknown. To address this problem we developed a numerical scheme enabling us to combine realistic magnetic stimulation (MS) with compartmental modeling of neurons with arbitrary morphology. The induced electric field for each location in space was combined with standard compartmental modeling software to calculate the membrane current generated by the electromagnetic field for each segment of the neuron. In agreement with previous studies, the simulations suggested that peripheral axons were excited by the spatial gradients of the induced electric field. In both peripheral and central neurons, MS amplitude required for action potential generation was inversely proportional to the square of the diameter of the stimulated compartment. Due to the importance of the fiber's diameter, magnetic stimulation of CNS neurons depolarized the soma followed by initiation of an action potential in the initial segment of the axon. Passive dendrites affect this process primarily as current sinks, not sources. The simulations predict that neurons with low current threshold are more susceptible to magnetic stimulation. Moreover, they suggest that MS does not directly trigger dendritic regenerative mechanisms. These insights into the mechanism of MS may be relevant for the design of multi-intensity TMS protocols, may facilitate the construction of magnetic stimulators, and may aid the interpretation of results of TMS of the CNS.     

Intraretinal axon diameter: a single cell analysis in the marmoset (Callithrix jacchus)

We have labelled individual retinal ganglion cells of a New World primate, the common marmoset (Callithrix jacchus) with neurobiotin and then measured axon, soma and dendritic field diameter. A total of 111 cells were analysed (62 parasol cells, 22 midget cells, 16 hedge cells and 11 small bistratified cells). When all retinal ganglion cells were grouped together axon diameter was positively correlated to soma diameter. When analysed according to cell class only midget cells showed a positive correlation between soma size and mean axon diameter. Dendritic field diameter and mean axon diameter of both parasol and midget cells showed significant correlations. Axon diameter is not constant along the intraretinal length of the axon and the rate of change in diameter appears to be related to the cell class and the initial size of the axon. Midget cell axons showed a rapid increase of up to 20% over the first 200 μm in contrast to parasol cell axons which increased more slowly over this distance but then showed a marked increase in diameter of up to 40% over the next 450 μm. However, axon diameter did not remain at these increased diameters but decreased at greater distances from the soma. The degree to which an axon changes its diameter is related to retinal ganglion cell class and the initial size of the axon. We postulate that these variations in intraretinal axon diameter may have a direct influence on conduction velocity and reflect a compensatory mechanism to minimise spatiotemporal dispersion along the visual pathway.     

Time Constants and Electrotonic Length of Membrane Cylinders and Neurons

A theoretical basis is provided for the estimation of the electrotonic length of a membrane cylinder, or the effective electrotonic length of a whole neuron, from electrophysiological experiments. It depends upon the several time constants present in passive decay of membrane potential from an initially nonuniform distribution over the length. In addition to the well known passive membrane time constant, τ_m = R_mC_m, observed in the decay of a uniform membrane potential, there exist many smaller time constants that govern rapid equalization of membrane potential over the length. These time constants are present also in the transient response to a current step applied across the membrane at one location, such as the neuron soma. Similar time constants are derived when a lumped soma is coupled to one or more cylinders representing one or more dendritic trees. Different time constants are derived when a voltage clamp is applied at one location; the effects of both leaky and short-circuited termination are also derived. All of these time constants are demonstrated as consequences of mathematical boundary value problems. These results not only provide a basis for estimating electrotonic length, L = [unk]/λ, but also provide a new basis for estimating the steady-state ratio, ρ, of cylinder input conductance to soma membrane conductance.