Effects of external currents on duration and amplitude of normal and prolonged action potentials from single nodes of Ranvier

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Duration and amplitude of normal and prolonged action potentials from single nodes of Ranvier vary as functions of potential changes induced by currents from an external source. The quantitative relations between externally applied potential and the resulting potential generated within the system are analyzed in order to obtain information about the kinetics of the electromotance,—potential,—and chemical changes taking place during excitation. The following preliminary conclusions are drawn: A depolarizing and a repolarizing process (positive and negative electromotance) increase and decrease with the potential. For a sudden potential displacement the negative electromotance reaches its new value at a faster rate than the positive electromotance. Since the individual values of the two electromotances depend on the potential and since they both generate a potential which is proportional to the difference of their absolute values, the values of either electromotance are determined by this difference as well as by any externally induced potential change.

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... The effect of maintained polarization upon the physiological properties of the node in potassium-rich media has been reported recently by Mueller (1958a) and by Stiimpfli (1958). They observed discontinuous variations in the membrane potential when the strength of the anodal polarizing current through the node was gradually increased. ...
... However, this sort of action potential has been reported to be elicited only under abnormal conditions. For instance, the hyperpolarizing response can be elicited only on prior depolarization of squid (Segal, 1958;Tasaki, 1959a), frog (Mueller, 1958;Stampfli, 1959;Liittgau, 1960), or toad (Tasaki, 1959a) axons. Although quantitative data on the kinetics of their electrogenetic processes are not as yet available, Grundfest (1960) suggested that these responses may develop as a result of reinstated UK-inactivation" when the K-conductance is first increased under experimental conditions. ...
The kinetics of interaction between potential, chemical equilibrium, and electromotance in the excitable system of nerve are analyzed. The theoretical system has the following properties: It gives rise to two electromotances each of which depends directly on a chemical equilibrium. The equilibria are determined by the potential across the system. After a sudden potential shift the equilibria reach their new value with an exponential time course, the time constant of which is determined by the rate constants of the two reactions. The rate constants are different due to different activation energies. The two electromotances give rise to potentials of opposite sign. The total potential produced by the system is equal to the sum of the two potentials. The two equilibria are thus determined by any externally applied potential as well as by the sum of the internally produced potentials. The dependence of the equilibria on the potential is calculated from first principles. The equations which describe this system are solved by an analogue computer, which gives instantaneous solutions of the total internal potential as a function of time and any voltage applied from an external source. Comparison between recorded and computed action potentials shows excellent agreement under all experimental conditions. The electromotances might originate from a Ca++—Na+—K+ exchange at fixed negative sites in the Schwann cell.
THE electrical properties of the myelinated nerve fibre in potassium-rich solution were observed by Stämpni1, Mueller2 and Tasaki3. Those of the unmyelinated nerve fibre were observed by Segal4, Tasaki3 and Moore5. When the membrane potential is depolarized by potassium, the potential difference across the membrane produced by the inward current pulse is larger than that produced by the outward one and exhibits a kind of discontinuous increase at a certain current intensity (the current-potential relation is non-linear). The time-course of the potential difference produced by the inward current has two steps. This phenomenon is called ``anodal threshold phenomenon'' by Segal4 and ``hyperpolarizing response'' by Tasaki3. Tasaki reported that the hyperpolarizing response in the giant axon of the squid was slightly different from that in the myelinated nerve fibre.
The crustacean single nerve fiber gives rise to trains of impulses during a prolonged depolarizing stimulus. It is well known that the alkaloid veratrine itself causes a prolonged depolarization; and consequently it was of interest to investigate the effect of this chemically produced depolarization on repetitive firing in the single axon and compare it with the effect of depolarization by an applied stimulating current or by a potassium-rich solution. It was found that veratrine depolarization, though similar in some respects to a potassium-rich depolarization of depolarizing current effect, was in many respects quite different.
1. An attempt was made to explain the extreme prolongation of the nodal action potential by 0.1–1.0 mM NiCl2 in terms of the ionic theory. 2. The effects of NiCl2 at room temperature are similar to those of temperature reduction: decreased maximum rate of rise of the action potential, lengthened action potential duration, elevated threshold, increased tendency for repetitive activity; in addition, the amplitude of the action potential is slightly increased. 3. The long lasting plateaus of the responses obtained under the combined influence of NiCl2 and temperature reduction are shortened by cathodal polarization, strong anodal polarization and decrease of [Na]o. The plateau can be prematurely terminated by short anodal pulses of critical amplitude; short cathodal pulses reduce the duration of the plateau gradually with increasing pulse strength. 4. Increased [K]o prolongs plateau duration; the steep repolarization phase which normally terminates the plateau is replaced by a long lasting after-depolarization with stepwise potential decline. The amplitude of K-depolarization is not influenced by NiCl2 or temperature reduction. 5. 1.0 mM NiCl2 changes the relation between maximum rate of rise and steady-state polarization; the potential change required for 50% sodium inactivation is +8 mV in normal Ringer's solution and +16 mV in the presence of 1.0 mM NiCl2 (22° C). 6. 1.0 mM NiCl2 increases the time constant of delayed rectification as measured in Na-poor solutions at 4° C by a factor of about 2. The decrease of action potential under cathodal polarization is slightly delayed by NiCl2. 7. It is concluded that prolongation of the nodal action potential by NiCl2 is due to delayed and reduced inactivation of sodium permeability and delayed increase of potassium permeability; part of the NiCl2-effect could be explained by assuming competition between Ni++ and Ca++ for specific sites at the membrane.
A ramp voltage clamp measurement described previously is used to detect alterations in the frog skin current-potential (I-V) characteristic following removal or replacement of various ions in the solutions bathing the skin. The ionic requirements for the maintenance of a negative-slope I-V property are the following: Ca(++), Na(+), and Cl(-) must be in the outside solution; K(+) and Cl(-) must be in the inside solution. Removal of any one of these ions from its respective solution results in the decay and eventual disappearance of the negative slope.The similarity between the I-V characteristic following Ca(++) removal with EDTA from the outside solution and the I-V relation in a refractory skin suggests that the loss (refractory state) and recovery of the negative slope is a consequence of unbinding and subsequent rebinding of Ca(++) to membrane sites. The role of the univalent ions is not clear-presumably some or all of these ions constitute the current through the skin; however, some of these ions may also be involved in maintaining a membrane condition necessary for the existence of a negative slope I-V relation. Further, excitation does not appear to be a direct consequence of the Na(+) pump.
Previous step voltage-clamp measurements on frog skin showed the presence of an N-shaped current-potential (I-V) relation in excitable skin. However, the collection and reconstruction of I-V data using discrete step changes of skin potential was tedious because of the long refractory period (up to 1 min) in frog skin. A direct and rapid (5 msec) method for recording the N-shaped I-V characteristic in real time is presented. Ramp functions are used as the command to the clamp system instead of a step function. Consequently the skin potential is forced to change in a linear manner (as commanded) and the skin current can be recorded as a continuous function of the controlled change of skin potential. With the ramp clamp, a low-resistance membrane state (〈 10 Ω · cm2) resembling a breakdown phenomenon was observed at high skin potential (〉 300 mv). Entry into the low resistance state resulted in a collapse of the N-shaped I-V relation to a nearly linear function. The utility of the ramp measurement is demonstrated by predicting (1) that the maximum rate of rise of the spike occurs at a voltage corresponding to the valley (local minimum) in the N-shaped I-V curve, (2) that the rate of rise of the spike increases with increasing clamp currents, (3) the voltage peak of the spike, and (4) the time course of the rising phase of the spike.
This report presents general principles of operations in neuron networks and is composed of two parts. One is concerned with the theoretical aspects of operations in neuron nets; the other is concerned with the application of some of these principles to the particular problem of speech recognition by artificial neurons. The term “neuron” is used without distinction for real neurons—those found in the brain—and for artificial neurons—those made from electronic components. It is possible to construct artificial neurons which are, as far as input- output relations are concerned, complete analogs of their biological counterpart (Mueller, 1958). The networks shown in the figures in this report have been assembled and tested using artificial neurons.
It is shown in a mathematical model of a myelinated nerve fiber that the development of a local response in an inexcitable node plays an important role in the mechanism of the "jumping" of an action potential (AP) across the inexcitable node. In the absence of such a response (for example, in the case of a 1000-fold decrease in the maximum sodium permeability, $$\bar P$$ Na) in fibers with normal relations between the length of the internodal segment (L) and its diameter (D) (L/D>100), the conduction is blocked. It is possible only in fibers with relatively short internodal segments (L/D
1. Current flow outward through the caudal, reactive membrane of the cell causes direct stimulation of the electroplaque. The electrical response in denervated as well as in normal preparations recorded with internal microelectrodes is first local and graded with the intensity of the stimulus. When membrane depolarization reaches about 40 mv. a propagated, all-or-nothing spike develops. 2. Measured with internal microelectrodes the resting potential is 73 mv. and the spike 126 mv. The latter lasts about 2 msec. and is propagated at approximately 1 M.P.S. 3. The latency of the response decreases nearly to zero with strong direct stimulation and the entire cell may be activated nearly synchronously. 4. Current flow inward through the caudal membrane of the cell does not excite the latter directly, but activation of the innervated cell takes place through stimulation of the nerve terminals. This causes a response which has a latency of not less than 1.0 msec. and up to 2.4 msec. 5. The activity evoked by indirect stimulation or by a neural volley includes a prefatory potential which has properties different from the local response. This is a postsynaptic potential since it also develops in the excitable membrane which produces the local response and spike. 6. On stimulation of a nerve trunk the postsynaptic potential is produced everywhere in the caudal membrane, but is largest at the outer (skin) end of the cell. The spike is initiated in this region and is propagated at a slightly higher rate than is the directly elicited response. Strong neural stimulation can excite the entire cell to simultaneous discharge. 7. The postsynaptic potential caused by neural or indirect stimulation may be elicited while the cell is absolutely refractory to direct excitation. 8. The postsynaptic potential is not depressed by anodal, or enhanced by cathodal polarization. 9. It is therefore concluded that the postsynaptic potential represents a membrane response which is not electrically excitable. Neural activation of this therefore probably involves a chemical transmitter. 10. The nature of the transmitter is discussed and it is concluded that this is not closely related to acetylcholine. 11. Paired homosynaptic excitation discloses facilitation which is not present when the conditioning stimulus is direct or through a different nerve trunk. These results may be interpreted in the light of the existence of a neurally caused chemical transmitter or alternatively as due to presynaptic potentiation. 12. The electrically excitable system of the electroplaque has two components. In the normal cell a graded reaction of the membrane develops with increasing strength of stimulation until a critical level of depolarization, which is about 40 mv. 13. At this stage a regenerative explosive reaction of the membrane takes place which produces the all-or-nothing spike and propagation. 14. During early relative refractoriness or after poisoning with some drugs (eserine, etc.) the regenerative process is lost. The membrane response then may continue as a graded process, increasing proportionally to the stimulus strength. Although this pathway is capable of producing the full membrane potential the response is not propagated. 15. Propagation returns when the cell recovers its regenerative reaction and the all-or-nothing response is elicited. 16. Excitable tissues may be classified into three categories. The axon is everywhere electrically excitable. The skeletal muscle fiber is electrically excitable everywhere except at a restricted region (the end plate) which is only neurally or chemically excitable. The electroplaque of the eel, and probably also cells of the nervous system have neurally and electrically excitable membrane components intermingled. The electroplaques of Raia and probably also of Torpedo as well as frog muscle fibers of the "slow" system have membranes which are primarily neurally and chemically excitable. Existence of a category of invertebrate muscle fibers with graded electrical excitability is also considered. 17. In the eel electroplaque and also probably in the cells of neurons, tests of the mode of neural activation carried out by direct or antidromic stimulation cannot reveal the neurally and chemically activated component. The data of such tests though they appear to prove electrical transmission are therefore inadequate for the detection and study of the chemically initiated process.
The duration of action potentials from single nodes of Ranvier can be increased by several methods. Extraction of water from the node (e.g. by 2 to 3 M glycerin) causes increased durations up to 1000 msec. 1 to 5 min. after application of the glycerin the duration of the action potential again decreases to the normal value. Another type of prolonged action potential can be observed in solutions which contain K or Rb ions at concentrations between 50 mM and 2 M. The nodes respond only if the resting potential is restored by anodal current. The kinetics of these action potentials is slightly different. Their maximal durations are longer (up to 10 sec.). Like the normal action potential, they are initiated by cathodal make or anodal break. They also occur in external solutions which contain no sodium. The same type of action potentials as in KCl is found when the node is depolarized for some time (15 to 90 sec., 100 to 200 mv.) and is then stimulated by cathodal current. These action potentials require no K or Na ions in the external medium. Their maximal duration increases with the strength and duration of the preceding depolarization. The possible origin of the action potentials in KCl and after depolarization, and their relation to the normal action potentials and the negative after-potential are discussed.
Ueber die Ausloesung rhythmischer und nichtrhythmischer Er-regtmgen im peripheren Nerven
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Elektrophysiologie der Herzmuskelfaser
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