The Problem of Excitability: Electrical Excitability and Ionic Permeability of the Nerve Membrane

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Depolarization of the resting membrane potential by reduced temperature. The experimental results could be reproduced in the computational model. The activation threshold was defined as the extracellular field alteration required to generate and action potential propagating to the end of the axon model.

In Fig.

Increased Excitability of Acidified Skeletal Muscle

Note the During cooling, all the ionic currents become slower, and the amplitudes are reduced see Fig. However, all amplitudes are not reduced equally for all currents, which in the computational model generated the increased excitability for the long durations of the stimulus. Ionic currents during an action potential generation. To study the contribution to the altered excitability of different subtypes of ionic currents, only one ionic current at a time was allowed to be influenced by the temperature change see Fig. For instance, the light blue line in Fig.

Additionally, the K Dr current may also contribute to the increase excitability to long durations of the electrical stimulation. The influence of temperature on subtypes of ionic currents. In pathological conditions, ionic currents may become abnormal and the excitability of nerve fibers related to reduced temperature may be altered. Increased knowledge of abnormal ionic currents in diabetic neuropathy patients may be obtained by comparing the perception thresholds, of different electrical stimulation, for different temperature conditions.

All four ionic currents have been implicated in diabetic neuropathy and been proposed as candidates for generating the increased excitability detected in small fibers [ 40 , 41 , 42 , 43 , 44 ]. The temperature was reduced in the computational models of hyperexcitability and the activation thresholds were re-estimated Fig. The relative change in activation threshold between the two temperature conditions for all models of hyperexcitability is illustrated in Fig. An increase of the Na P current generated a similar behavior Fig. Cooling may increase understanding of abnormal ionic current during neuropathy.

However, no significant effect was observed for the shorter pulse durations.


The computational model indicated that depolarization occurred when the temperature was reduced. Both patch clamp experiment of small dorsal root ganglion somas, as well as threshold tracking of the compounded action potential of large nerve fibers in humans, support that a depolarization of the cell membrane occurs when the temperature is reduced [ 25 , 26 , 27 ].

Moreover, the mechanisms for generating the depolarization of the cell membrane during a reduced temperature has not been identified. In threshold tracking experiment of the compound action potential in large fibers, the excitability alteration due to temperature change has been studied [ 26 , 27 ]. The selective effect of cooling on long durations of the electrical stimuli may be due to increased time constants of the Na TTXr , which is selectively expressed in nociceptive fibers, where it generates the action potential [ 39 ]. In large fibers, non-nociceptors, the Na TTXs current is generating the action potential in nodes of Ranvier.

Therefore, cooling of the skin may increase excitability of nociceptors selectively and therefore promote preferential activation of nociceptors by cutaneous electrodes. Excitability of small fibers is usually studied through microneurography, which is technically challenging and time consuming due to the small fiber size. Our research group has developed the PTT technique, which is an inexpensive and non-invasive alternative method to indirectly assess the excitability of the cell membrane of both small and large fibers [ 10 , 17 ].

In the current study, it was possible to detect the excitability change due to reduced temperature with the PTT technique and thereby increase the support for the usage of the PTT technique to assess the membrane excitability in nerve fibers. Moreover, the result from the computational study supports that cooling simultaneous with electrical stimulation may increase the knowledge of abnormal ionic membrane currents occurring in neuropathic pain patients. It would be interesting to evaluate whether the reduced perception threshold for long pulse durations due to cooling would be less reduced in this patient group compared to healthy participants as studied in the current study.

The pulse had an increasing form of bounded exponential current, which for long durations has been shown to elevate the perception threshold of large fibers but not for small fibers [ 17 ]. This most likely reflects accommodation of large fibers, which has been reported for identical electrical pulse shape [ 45 ] and linearly increasing pulses [ 46 ]. It should be noted that for standard rectangular pulses, large fibers are recruited prior to small fibers [ 47 ] and therefore, the pulse shape applied in current study is considered more preferential towards the small fibers.

The preferential activation of small fibers with the planar array electrode has not been evaluated. However, similar small area cathodes have been used to activate small fibers preferentially [ 5 , 7 , 9 , 10 , 17 ]. Additional support for the Planar array electrode preferential activation of small fibers is the lack of accommodation to slowly rising electrical pulses.

The basis for the use of the Planar array electrode in the current study was its flat dimensions, which makes it possible to use a thermode to regulate the temperature, which is an essential part of this study. This feature separates it from currently available pin electrodes, as the dimensions of these electrodes do not allow for the thermode to be placed on top of the electrode for cooling.

Instead, our focus is on the effect of cooling on other ionic currents in the peripheral part of small fibers by using electrical stimulation as test stimulus. The recorded alterations of perception thresholds to the electrical pulses in the current study are dependent on the duration of the electrical input. It is therefore reasonable to assume that the electrical stimulation, rather than the reduced temperature, mainly activated the fibers. Cutaneous electrical stimulation alters the membrane potential without activation of sensory transduction within sensory terminals.

Small cathode electrodes generate a high current density in epidermis where the small fibers terminate [ 11 , 12 , 13 , 14 , 15 , 16 ]. The small influence on the perception threshold from cold sensing fibers can be explained by the fact that only a small proportion of the fibers express the cool-sensitive transduction channels.

A recent study by Luiz et al. Therefore, only a small part of the depolarization predicted by the computational model could originate from cold sensing nerves. The perception threshold was used as an indirect measurement of the excitability of the cell membrane. To avoid sensitizing the central nervous system low frequency and intensity was used in the current study since high frequency and intensity has been used to induce long term potentiation-like sensitization of the central nervous system [ 7 ].

Other central nervous system effects such as expectation and attention are probably the same for the different durations of the electrical stimuli. The repeated low intensity pulses might have caused habituation as observed in a recent study [ 50 ]. Therefore, to overcome this limitation, the order of pulse durations was randomized, as well as the two temperature conditions.

Habituation also occurs to the cold stimulus, but is likely limited due to relatively high temperature applied in the current study [ 51 ]. One of the limitations of the computational model is that the axon model has a reduced morphology, which may affect the validity of the model results. Furthermore, the computational model did not include the influence of the electrical properties of the skin. The study showed that cooling of the skin decreased the perception threshold particularly for the long duration of slowly increasing pulses. Cooling may alter the ionic current during electrical stimulation and thereby provide additional information regarding membrane excitability of small fibers.

The PTT technique could detect the excitability alteration occurring during reduced temperature and may have the ability to become a diagnostic tool for neuropathy. The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. Double and triple spikes in C nociceptors in neuropathic pain states: an additional peripheral mechanism of hyperalgesia.

Microneurographic identification of spontaneous activity in C-nociceptors in neuropathic pain states in humans and rats. Bromm B, Meier W. The intracutaneous stimulus—a new pain model for algesimetric studies. Methods Find Exp Clin Pharmacol. Nilsson HJ, Schouenborg J. Differential inhibitory effect on human nociceptive skin senses induced by local stimulation of thin cutaneous fibers.

A new method to increase nociception specificity of the human blink reflex. Clin Neurophysiol. Perceptual correlates of nociceptive long-term potentiation and long-term depression in humans. J Neurosci. Selective stimulation of C fibers by an intra-epidermal needle electrode in humans. Open Pain J. Differences in perception and brain activation following stimulation by large versus small area cutaneous surface electrodes. Eur J Pain. Membrane properties in small cutaneous nerve fibers in humans.

Muscle Nerve. Ultrastructural evidence for nerve fibers within all vital layers of the human epidermis. J Invest Dermatol. Denervation of skin in neuropathies: the sequence of axonal and Schwann cell changes in skin biopsies. Myelinated nerve endings in human skin. Estimating nerve excitation thresholds to cutaneous electrical stimulation by finite element modeling combined with a stochastic branching nerve fiber model. Med Biol Eng Comput. Inui K, Kakigi K. Pain perception in humans: use of intraepidermal electrical stimulation. J Neurol Neurosurg Psychiatry.

Evaluating dermal myelinated nerve fibers in skin biopsy. Evaluating the ability of non-rectangular electrical pulse forms to preferentially activate nociceptive fibers by comparing perception thresholds. Scand J Pain. Lawson K.

The Problem of Excitability : B. I. Khodorov :

Such situation with similar permeabilities for counter-acting ions, like potassium and sodium in animal cells, can be extremely costly for the cell if these permeabilities are relatively large, as it takes a lot of ATP energy to pump the ions back. Because no real cell can afford such equal and large ionic permeabilities at rest, resting potential of animal cells is determined by predominant high permeability to potassium and adjusted to the required value by modulating sodium and chloride permeabilities and gradients.

In a more formal notation, the membrane potential is the weighted average of each contributing ion's equilibrium potential. The size of each weight is the relative conductance of each ion. In the normal case, where three ions contribute to the membrane potential:. For determination of membrane potentials, the two most important types of membrane ion transport proteins are ion channels and ion transporters.

Ion channel proteins create paths across cell membranes through which ions can passively diffuse without direct expenditure of metabolic energy. They have selectivity for certain ions, thus, there are potassium- , chloride- , and sodium-selective ion channels. Different cells and even different parts of one cell dendrites , cell bodies , nodes of Ranvier will have different amounts of various ion transport proteins.

Typically, the amount of certain potassium channels is most important for control of the resting potential see below. Most pumps use metabolic energy ATP to function. Most cells have potassium-selective ion channel proteins that remain open all the time. There will be net movement of positively charged potassium ions through these potassium channels with a resulting accumulation of excess negative charge inside of the cell.

The outward movement of positively charged potassium ions is due to random molecular motion diffusion and continues until enough excess negative charge accumulates inside the cell to form a membrane potential which can balance the difference in concentration of potassium between inside and outside the cell.

A good approximation for the equilibrium potential of a given ion only needs the concentrations on either side of the membrane and the temperature. It can be calculated using the Nernst equation :. Differences are observed in different species, different tissues within the same animal, and the same tissues under different environmental conditions.

The units used for concentration are unimportant as they will cancel out into a ratio. For Potassium at normal body temperature one may calculate the equilibrium potential in millivolts as:. At physiological temperature, about The resting membrane potential is not an equilibrium potential as it relies on the constant expenditure of energy for ionic pumps as mentioned above for its maintenance.

It is a dynamic diffusion potential that takes this mechanism into account—wholly unlike the equilibrium potential, which is true no matter the nature of the system under consideration. The resting membrane potential is dominated by the ionic species in the system that has the greatest conductance across the membrane. For most cells this is potassium.

As potassium is also the ion with the most negative equilibrium potential, usually the resting potential can be no more negative than the potassium equilibrium potential. The resting potential can be calculated with the Goldman-Hodgkin-Katz voltage equation using the concentrations of ions as for the equilibrium potential while also including the relative permeabilities of each ionic species. Secretion, mostly as the mechanism responsible for excitatory or inhibitory synaptic transmission, will be dealt in other entries. When considering neuronal function, electrical excitability is indeed one of the main themes of concern.

Passive properties refer to the capacitative and resistive aspects inherent in neuronal membranes, along with the resistivity inherent in the cytoplasm and the extracellular milieu.

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Together, these properties provide an electrical resemblance between neuronal processes axons and dendrites and conduction in electrical cables and hence are termed cable properties. While the basic assumption of most electrophysiologists is that the membrane potential may be initially considered as having a resting value the resting potential that is uniformly distributed along neuronal compartments, this is an oversimplification, as the ionic conductances and pumps which are responsible for setting the resting potential need not have a fixed density throughout the neuronal membrane.

Even so, isopotentiality is inherent in most initial cable property assumptions. The value of the electrical field in mV is related to the driving force emf for each of the ionic species that can move across the membrane and the magnitude of the conductance for each ionic species i. While a more or less uniform permeability may be found for the leakage channels a constantly open channel permeable to potassium , voltage gated channels allowing sodium, potassium, calcium, and chloride ions across the plasmalemma also contribute to the membrane potential to the extent of the magnitude of their conductance at a given time.

Note however that these latter conductances, because they are voltage-gated, deviate from the simple passive character of the leakage channel. Because of the complexity afforded by the branching pattern of the dendritic tree, the passive electrical properties of neurons were initially difficult to envision without a proper mathematical model. In the mid sixties of last century Wilfred Rall see Rall Model was the first to define the electrotonic cable properties of branching dendritic trees and to show the importance of such branching patterns on synaptic summation at different sites in the dendritic arbor.

Neurons conduct waves of membrane potential passively electrotonically a short distance along their processes as the result of currents that flow intracellularly along the longitudinal resistance and simultaneously across the plasmalemmal membrane as resistive or capacitative current. When active properties are engaged these changes can travel the entire length of these processes. By active electrical properties it is meant that the electrical potentials across the plasma membrane may be affected by the activation of voltage, ligand, or second messenger gated transmembrane ionic channels.

The generation of action potentials is an example of electrical properties brought about by active, voltage-dependent means.

The Excitable Cell And Resting Membrane Animation

Here the electric field across the membrane will act on the voltage sensors of transmembrane ionic channels channel sites with dipole moment properties that will trigger conformational changes, often allosteric, that will change channel ionic conductance. In the specific case of action potentials voltage-gated channels, the inflow of sodium or calcium ions depolarizes the plasma membrane.

In turn, opening voltage-gated potassium channels and the resulting current flow repolarizes the plasma membrane. Although the conductance of most voltage-gated channels are increased by membrane depolarization, the conductance of some channels is increased when the membrane is hyperpolarized. Other examples of active electrical properties are those brought about by ligand-gated ionic conductances, where the binding of a neurotransmitter will gate ionic conductances allowing the generation of excitatory or inhibitory synaptic potentials. Yet another form of electrical activity is represented by intrinsic subthreshold oscillations, where the excitability of the cell is gated in such a fashion that the membrane potential is not uniform but rather in a state of continuous fluctuation , generating an oscillatory sinusoidal-like membrane profile—often with phase reset properties indicating chaotic, dynamic kinetics.

In an active neuron the superposition of passive and active electrical properties serves to allow the cell the possibility of summing the transmembrane potential either linearly or non-linearly and to reach depolarization levels sufficiently high to trigger action potentials. These can be conducted either along the length of the axon or dendritic tree, in an all-or-none continuous manner, in a saltatory fashion, or in a decremental mode.

Neurons have but one axon, that is, a single process leaving the soma or a dendrite. However, axons branch either in the form of collaterals along the axonal length or at a terminal arborization known as the telodendrion distal dendrite. These terminals are usually the site of presynaptic boutons that establish synaptic contacts with other neurons, muscles, or glands. Because they originate from a single initial segment axons send very similar spike sequences to all their branches. However, spike failure at branch points or changes in conduction velocity, secondary to changes in axonal diameter after branching, can reset conduction patterns and conduction times.

A good example is the isochrony of spike conduction time found in the axons from the inferior olive that terminate in the cerebellum as what is called climbing fibers. In addition to action potentials in axons, dendrites may also generate regenerative events.


For the most part these potentials decrement with distance but may reach the most distal dendritic branches See Figure 7. Such action potentials can be centripetal towards the soma or centrifugal back propagating away from the soma depending on the dendritic morphology and the distribution and density of voltage gated ionic channels over the dendritic tree.

For more information, see Dendrites , Dendritic spikes , and Dendritic processing. Beyond action potentials and synaptic transmission there is the question of the electrical activity generated autonomously by neurons.