Theoretical response to trains of action potentials of a bifurcating axon with one short daughter branch.

It has been shown both experimentally (Stockbridge, N., and L. L. Stockbridge. 1988. J. Neurophysiol. 59:1277-1285) and theoretically (Stockbridge, N. 1988. J. Neurophysiol. 59:1286-1295) that the second of two closely spaced action potentials may be differentially conducted into a short daughter branch. Using numerical methods, the response to trains was examined in axons with a single bifurcation and uniform membrane properties. Short daughter branches conduct at higher rates of stimulation than do long branches. Under some conditions the longer daughter branch is always silent. Under other conditions, one or both branches will begin to conduct action potentials only when the stimulus frequency is high enough.     

Squid giant axons. A model for the neuron soma?

Insertion of electrically floating wires along the axis of a squid giant axon produces an apparent increase in diameter in the region where the wire surface has been treated to give it a low resistance. The shape of action potentials propagating into this region depend upon the surface resistance (and the length) of the wire. As this segment's internal resistance is lowered by reducing the wire's surface resistance, the following characteristic sequence of changes in the action potential is seen at the transition region: (a) the duration increases; (b) two peaks develop, the first one generated in the normal axon region and the second one generated later in the axial wire region, and; (c) blockage occurs (for a very low resistance wire). Action potentials recorded at the membrane region near the tip of the axial wire in (b) resemble those recorded at the initial segment of neurons upon antidromic invasions. Squid axon action potentials propagated from a normal region into that containing the low resistance wire also resemble antidromic invasions recorded in neuron somas. Hyperpolarizing current pulses applied through the wire act as if the wire surface resistance was momentarily reduced. For example, the two components of the action potential recorded at the axial wire membrane region noted in (b) can be sequentially blocked by the application of increasing hyperpolarizing current through the wire. Similar effects are seen when hyperpolarizing currents are injected into motoneuron somas. It is concluded that the geometrical properties of the junction of a neuron axon with its soma may be in themselves sufficient to determine the shape of the action potentials usually recorded by microelectrodes.     

Propagation of action potentials in squid giant axons. Repetitive firing at regions of membrane inhomogeneities

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.     

Repetitive activity of a branched Hodgkin-Huxley axon with multiple encoding sites

Afferent activity in a receptor afferent fiber with several encoding sites is generally believed to represent the activity of the fastest pacemaker that resets all more slowly encoding sites. Alternatively, some impulse mixing as well as some nonlinear summation of receptor current to a single encoder have been considered. In this article the repetitive firing activity of a Hodgkin-Huxley axon consisting of two branches that join into a single stem axon was investigated. The model axon was stimulated by constant-current injection into either the right or the left or both branches. It was found that the model axon generated an (infinite) train of action potentials if the input current was large enough. The discharge frequency found was constant, and on combined stimulation of both branches with different current, the site of impulse initiation was always in the branch receiving the higher input current, excluding a simple impulse mixing. On the other hand, the combined stimulation of both branches evoked repetitive firing with a higher frequency than expected by the pacemaker-resetting hypothesis. Moreover, a stimulus that is subthreshold for repetitive firing if injected into one branch yields repetitive firing when it is injected into both branches, a behavior inconsistent with impulse mixing and pacemaker resetting. On the other hand, current injection into one branch allowed repetitive activity only within a rather limited range of firing frequencies. Using distributed current injection into both branches, however, allowed many more different firing frequencies. Such behavior is inconsistent with both pacemaker resetting and (nonlinear) input current summation. Consequently, the repetitive firing behavior of a branched Hodgkin-Huxley axon with multiple encoding sites appears to be more complex than postulated in the simple hypotheses.     

Laser microbeam axotomy and conduction block show that electrical transmission at a central synapse is distributed at multiple contacts

Touch (T) sensory neurons in the leech innervate defined regions of skin and synapse on other neurons, including other T cells, within the ganglionic neuropil. The cells' receptive fields in the periphery are comprised of a central region, innervated by thick axons, and adjoining regions (minor fields) innervated by thinner axons. Secondary branches, known to be sites of synapses, emerge from the thinner and thicker axons. Pairs of T cells appear to make up to 200 separate contacts distributed within the neuropil. When the T cell is hyperpolarized, as occurs during natural stimulation of the cell, action potentials generated in the minor field and travelling into the ganglion along the thin axons may fail to conduct at central branch points. Evidence is presented, using axon conduction block and laser axotomy of cells filled with 6-carboxy-fluorescein, that synapses between separate groups of branches can function independently. Thus, selective activation of branches of the thin anterior axon produced a synaptic potential 36 +/- 6% of control amplitude, which was consistent with counts of 39 +/- 6% of contacts made by these branches. Laser axotomy of postsynaptic neurons showed that the anterior contacts indeed made the principal or only contacts activated during anterior conduction block. The results show that conduction block can modulate transmission within the ganglion, and it operates by silencing particular contacts between cells.     

Fast-axon synapses of a crab leg muscle

Neuromuscular synapses of the "fast" excitatory axon supplying the main extensor muscle in the leg of the shore crab Pachygrapsus crassipes were studied with electrophysiological and electron-microscopic techniques. Electrical recording showed that many muscle fibers of the central region of the extensor muscle responded only to stimulation of the fast axon, and electron microscopy revealed many unitary subterminal axon branches. Maintained stimulation, even at a low frequency, resulted in depression of the excitatory junctional potentials (EJPs) set up by the fast axon but EJPs of different muscle fibers depressed at different rates, indicating some physiological heterogeneity among the fast-axon synapses. Focal recording at individual synaptic sites on the surfaces of the muscle fibers showed quantal contents ranging from 1.4 to 5.5 at different synapses; these values are relatively high in comparison with similar determinations made in the crayfish opener muscle. Synapse-bearing nerve terminals were generally relatively small in diameter and filiform, with many individual synaptic contact areas of uniform size averaging 0.6 micron2. All of the individual synapses had a presynaptic "dense body" at which synaptic vesicles clustered. If these structures represent release points for transmitter quanta, the initial high quantal content would have an ultrastructural basis. The mitochondial content of the nerve terminals, the synaptic vesicle population, and the specialized subsynaptic sarcoplasm were all much reduced in comparison with tonic axon synaptic regions in this and other crustaceans. The latter features may be correlated with the relatively infrequent use of this axon by the animal, and with rapid fatigue.     

Antidromic propagation of action potentials in branched axons: implications for the mechanisms of action of deep brain stimulation

Electrical stimulation of the central nervous system creates both orthodromically propagating action potentials, by stimulation of local cells and passing axons, and antidromically propagating action potentials, by stimulation of presynaptic axons and terminals. Our aim was to understand how antidromic action potentials navigate through complex arborizations, such as those of thalamic and basal ganglia afferents-sites of electrical activation during deep brain stimulation. We developed computational models to study the propagation of antidromic action potentials past the bifurcation in branched axons. In both unmyelinated and myelinated branched axons, when the diameters of each axon branch remained under a specific threshold (set by the antidromic geometric ratio), antidromic propagation occurred robustly; action potentials traveled both antidromically into the primary segment as well as "re-orthodromically" into the terminal secondary segment. Propagation occurred across a broad range of stimulation frequencies, axon segment geometries, and concentrations of extracellular potassium, but was strongly dependent on the geometry of the node of Ranvier at the axonal bifurcation. Thus, antidromic activation of axon terminals can, through axon collaterals, lead to widespread activation or inhibition of targets remote from the site of stimulation. These effects should be included when interpreting the results of functional imaging or evoked potential studies on the mechanisms of action of DBS.     

Finding the optimal lengths for three branches at a junction

This paper presents an exact analytical solution to the problem of locating the junction point between three branches so that the sum of the total costs of the branches is minimized. When the cost per unit length of each branch is known the angles between each pair of branches can be deduced following reasoning first introduced to biology by Murray. Assuming the outer ends of each branch are fixed, the location of the junction and the length of each branch are then deduced using plane geometry and trigonometry. The model has applications in determining the optimal cost of a branch or branches at a junction. Comparing the optimal to the actual cost of a junction is a new way to compare cost models for goodness of fit to actual junction geometry. It is an unambiguous measure and is superior to comparing observed and optimal angles between each daughter and the parent branch. We present data for 199 junctions in the pulmonary arteries of two human lungs. For the branches at each junction we calculated the best fitting value of x from the relationship that flow ∞ (radius)^x. We found that the value of x determined whether a junction was best fitted by a surface, volume, drag or power minimization model. While economy of explanation casts doubt that four models operate simultaneously, we found that optimality may still operate, since the angle to the major daughter is less than the angle to the minor daughter. Perhaps optimality combined with a space filling branching pattern governs the branching geometry of the pulmonary artery.     

Redistribution of water via layering branches between connected parent and daughter trees in Norway spruce clonal groups

Key message

We measured sap flow and shoot water potentials in clonally connected parent and daughter trees. We found bidirectional flow patterns in branches mediating the connection between parent and daughter trees.

Abstract

Layering is an important mode of vegetative reproduction at treeline, in which clonal daughter trees are formed by the rooting of lower (“layering”) branches of the parent tree. These branches mediate the connection between parent (PT) and daughter tree (DT). Here, we measured quantity and direction of sap flow in layering branches as well as PT and DT, and measured shoot water potentials in the crowns of a connected PT and DT. We found bidirectional sap flow pattern in layering branches, with the bidirectionality of the flow resulting from water potential dynamics of the parent and daughter trees varying diurnally. We found that 4.3 % of the total water transpired by the DT was supplied by the PT root system, with up to 25 % of the instantaneous daughter tree sap flow coming from the parent tree. In contrast, water provided by the daughter’s root system to the parent tree comprised only a negligible amount, less than 1 % of the parent’s entire sap flow. Additionally, after experimental excavation of part of the DT roots, layering branch flow towards the DT increased, while flows in the opposite direction almost vanished. This study showed that aboveground clonal connections can facilitate a new type of hydraulic redistribution where water is transported bidirectionally through branches. This transfer of water and nutrients is vital especially in the first years of the daughter tree but supplies considerable amounts of water even several years after the establishment of a new clonal tree.

     

Simple models of stimulation of neurones in the brain by electric fields

The excitation of pyramidal cells in the motor cortex, produced by electric fields generated by distant electrodes or by electromagnetic induction, has been modelled. Linear, steady-state models of myelinated axons capture most of the geometrical aspects of neurone activation in electric fields. Some non-linear features can be approximated. Models with a proximal sealed-end and distal infinite axon, or of finite length, are both serviceable. Surface anodal stimulation produces hyperpolarisation of the proximal axon (closest to the anode) and depolarisation in the distal axon. The point of maximum depolarisation can be influenced by the location of the cathode (greater separation of anode and cathode causes more distal depolarisation). Axon bends can produce very localised depolarisation. Cathodal stimulation may be less effective than anodal as a result of anodal block of conduction of action potentials in the distal axon. The latencies of responses to anodal stimulation, recorded in the distal axon, will decrease as the stimulus strength is increased and the point of action potential initiation moves distally node by node. Larger jumps in latency will be produced when the point of action potential initiation moves from one axon bend to another.     

Action of different toxins from the scorpion Androctonus australis on a locust nerve-muscle preparation

The neuromuscular effects of four purified toxins and crude venom from the scorpion Androctonus australis were investigated in the extensor tibiae nerve-muscle preparation of the locust Locusta migratoria. Insect and crustacean toxin and the mammal toxins I and II which have previously been shown to act on fly larvae, isopods, and mice all paralyse locust larvae. The paralytic potencies decrease in the following order: insect toxin → mammal toxin I → crustacean toxin → mammal toxin II.The toxins and crude venom cause repetitive activity of the motor axons. This leads to long spontaneous trains of junction potentials in the case of crude venom and insect toxin. The other toxins chiefly cause short bursts of action and junction potentials following single stimuli.The ‘slow’ excitatory motor axon invariably is affected sooner than the inhibitory or the ‘fast’ excitatory one. The minimal doses of toxins required to affect the ‘slow’ motor axon decrease in an order somewhat different from that established for their paralytic potencies: insect toxin → crustacean toxin → mammal toxin I → mammal toxin II.Crude venom depolarises and destabilises the muscle membrane potential at low doses. At high doses it decreases the membrane resistance, whereas insect toxin leads to an increase.Crude venom and insect toxin enhance the frequency of mejps, whereas mammal toxin I leads to the occurrence of ‘giant’ mejps.The pattern of axonal activities indicates that the various peripheral branches of the motor nerve are the primary target of the toxins.The time course of nerve action potentials is affected by mammal toxin I and crustacean toxin which cause anomalous shapes and prolongations not caused by insect toxin.The results with other animals suggest that only the insect toxin is selective in its activity. The way it affects the axon might be quite different from that previously reported for scorpion venoms or toxins.     

Internal perfusion of crayfish, giant axons: action of tannic acid, DDT, and TEA

Crayfish giant axons remain viable following internal perfusion with a mixture of fluoride and citrate salts. The relative favorability of various internal anions, and the dependence of resting and action potentials on internal cations are both similar to results on internally perfused squid axons. TEA widens the falling phase of the spike only from inside the axon, while DDT is active from either side of the membrane. Records of impedance changes show that effects of TEA and DDT on components of ionic conductances are similar to those found in other axons by voltage clamp measurements. Tannic acid perfused internally at a concentration of the order of 10 μM produces spontaneous activity, and a progressive increase in spike width. After 30 minutes, action potentials are “cardiac” type and are up to several minutes in duration. Records of impedance changes, and data from rapid changes in external ionic concentrations, suggest that the plateau phase of the spike is due to a maintained increase in sodium conductance. Since tannic acid is capable of crosslinking proteins and “rigidifying” protein monolayers, it is suggested that its effects on the axon may be the result of an interference with a conformational change in a membrane protein or protein-phospholipid complex during excitation.     

The sites for mechano-electric conversion in a Pacinian corpuscle

The sensory nerve ending in the Pacinian corpuscle is surrounded by a non-nervous capsular structure which occupies about 99.9 per cent of the corpuscle's entire mass. After extirpation of practically all of the non-nervous structure, the sense organ's remains continue to function as a mechano-receptor, namely to produce generator and all-or-nothing potentials in response to mechanical stimuli. Compression of the first intracorpuscular node of Ranvier abolishes the production of "all-or-nothing" potentials in the corpuscle. Graded generator potentials constitute then the only response to mechanical stimulation. This reveals that the first node is the site of origin of the all-or-nothing potential and that the non-myelinated ending is incapable of producing all-or-nothing responses in response to mechanical stimulation. Compression of the entire length of non-myelinated ending suppresses the production of generator potentials. Partial compression of the ending abolishes mechano-responsiveness only of the compressed part. The intact remains of the ending continue to give generator potentials upon mechanical stimulation. This suggests that the generator potential arises at functionally independent membrane parts distributed all over the non-myelinated nerve ending. 24 to 36 hours after denervation of the corpuscle by transection of its sensory axon, no sign of electric activity is detected. Failure of mechano-reception at the nerve ending precedes that of conduction at the degenerating myelinated axon.     

Seasonal variation in conduction velocity of action potentials in squid giant axons

To determine whether the electrical properties of the squid giant axon are seasonally acclimated, action potentials, recorded at different temperatures, were compared between giant axons isolated from Loligo pealei caught in May, from relatively cold waters (approximately 10 degrees-12 degrees C), and in August, from relatively warm waters (approximately 20 degrees C). Parameters relating to the duration of the action potential (e.g., maximum rate of rise, maximum rate of fall, and duration at half-peak) did not change seasonally. The relationship between conduction velocity and temperature remained constant between seasons as well, in spite of the fact that May axons were significantly larger than August axons. When normalized to the fiber diameter, mean May conduction velocities were 83% of the August values at all temperatures tested, and analysis of the rise time of the action potential foot suggested that a change in the axoplasmic resistivity was responsible for this difference. Direct measurements of axoplasmic resistance further supported this hypothesis. Thus seasonal changes in the giant axon's size and resistivity are not consistent with compensatory thermal acclimation, but instead serve to maintain a constant relationship between conduction velocity and temperature.     

Physiological and morphological identification of photosensitive neurons in the opisthosomal ganglia of Limulus polyphemus

The motor outputs of the isolated opisthosomal ventral nerve cord in Limulus polyphemus are modulated by light. We have identified the photosensitive neurons and examined their physiological and morphological properties using intracellular recording and staining techniques. We found that photosensitive neurons are present in each ganglion of the opisthosomal ventral nerve cord. These neurons often discharged action potentials spontaneously in the dark, and they increased the frequency of this discharge in the light. The mean latency (+/-SD) of the light-induced action potential was 2.2 +/- 1.1 s. Cells responded in a graded fashion over a 2-log unit of light intensity. The peak spectral sensitivity was 425 nm or lower. The Lucifer-yellow-labeled photosensitive neurons had oval somata with mean (+/-SD) diameters of 102 +/- 3 microm (long axis) and 75 +/- 5 microm (short axis), and extended their axons to the contralateral region of the ventral nerve cord. The soma had no dendrites, and the axon had thin branches.     

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.     

Effects of external ions on membrane potentials of a crayfish giant axon

Transmembrane potentials in the crayfish giant axon have been investigated as a function of the concentration of normally occurring external cations. Results have been compared with data already available for the lobster and squid giant axons. The magnitude of the action potential was shown to be a linear function of the log of the external sodium concentration, as would be predicted for an ideal sodium electrode. The resting potential is an inverse function of the external potassium concentration, but behaves as an ideal potassium electrode only at the higher external concentrations of potassium. Decrease in external calcium results in a decrease in both resting potential and action potential; an increase in external calcium above normal has no effect on magnitude of transmembrane potentials. Magnesium can partially substitute for calcium in the maintenance of normal action potential magnitude, but appears to have very little effect on resting potential. All ionic effects studied are completely reversible. The results are in generally good agreement with data presently available for the lobster giant axon and for the squid giant axon.     

Numerical study on flows of red blood cells with liposome-encapsulated hemoglobin at microvascular bifurcation

Flow analysis at microvascular bifurcation after partial replacement of red blood cell (RBC) with liposome-encapsulated hemoglobin (LEH) was performed using the lattice Boltzmann method. A two-dimensional symmetric Y bifurcation model with a parent vessel diameter of 20 mum and daughter branch diameters of 20 microm was considered, and the distributions of the RBC, LEH, and oxygen fluxes were calculated. When only RBCs flow into the daughter branches with unevenly distributed flows, plasma separation occurred and the RBC flow to the lower-flow branch was disproportionately decreased. On the other hand, when half of RBC are replaced by LEH, the biasing of RBC flow was enhanced whereas LEH flowed favorably into the lower-flow branch, because many LEH within the parent vessel are suspended in the plasma layer, where no RBCs exist. Consequently, the branched oxygen fluxes became nearly proportional to flows. These results indicate that LEH facilitates oxygen supply to branches that are inaccessible to RBCs.     

Subepicardial phase 0 block and discontinuous transmural conduction underlie right precordial ST-segment elevation by a SCN5A loss-of-function mutation

Two mechanisms are generally proposed to explain right precordial ST-segment elevation in Brugada syndrome: 1) right ventricular (RV) subepicardial action potential shortening and/or loss of dome causing transmural dispersion of repolarization; and 2) RV conduction delay. Here we report novel mechanistic insights into ST-segment elevation associated with a Na(+) current (I(Na)) loss-of-function mutation from studies in a Dutch kindred with the COOH-terminal SCN5A variant p.Phe2004Leu. The proband, a man, experienced syncope at age 22 yr and had coved-type ST-segment elevations in ECG leads V1 and V2 and negative T waves in V2. Peak and persistent mutant I(Na) were significantly decreased. I(Na) closed-state inactivation was increased, slow inactivation accelerated, and recovery from inactivation delayed. Computer-simulated I(Na)-dependent excitation was decremental from endo- to epicardium at cycle length 1,000 ms, not at cycle length 300 ms. Propagation was discontinuous across the midmyocardial to epicardial transition region, exhibiting a long local delay due to phase 0 block. Beyond this region, axial excitatory current was provided by phase 2 (dome) of the M-cell action potentials and depended on L-type Ca(2+) current ("phase 2 conduction"). These results explain right precordial ST-segment elevation on the basis of RV transmural gradients of membrane potentials during early repolarization caused by discontinuous conduction. The late slow-upstroke action potentials at the subepicardium produce T-wave inversion in the computed ECG waveform, in line with the clinical ECG.     

End plate spikes in the human electromyogram. Revision of the fusimotor theory.

'End plate spike' (EPS) is a spontaneous action potential of a normal striated muscle. EPSs are found in local 'active spots' of the muscle. The prevailing hypothesis about the origin of EPSs states that when a needle electrode affects a motor nerve branch near the neuromuscular junction at the end plate zone, an increased leakage of acetylcholine to the synaptic cleft ensues. This elicits postsynaptic action potentials of the muscle fibre which can be recorded as EPSs with the same needle electrode. Thus EPSs are thought to be caused by needle injury or irritation of the motor axon. We suggest that EPSs are action potentials of intrafusal muscle fibres and that 'active spots' are in fact muscle spindles. Waveform analysis reveals three types of EPSs: small EPSs, not propagated outside the active spot either: i) with negative onset; or ii) with short positive initial deflection; and iii) large EPSs resembling propagated motor unit potentials (MUPs) but with a typical EPS firing pattern, distinctly different from that of the MUPs. Study of EPS activation in different manoeuvres associates small EPSs with intrafusal gamma motor units and large MUP-like EPSs with beta motor units.