›

Neuronal Excitation

Notes

Neuronal Excitation

Sections






Overview

Here, we'll learn fundamental aspects of neuronal excitation.

Key Definitions

  • Start a table.

Denote that we'll learn the definitions for several key, interrelated mediators of cellular physiology:

  • Electrochemical gradient
  • Equilibrium potential V(eq)
  • Membrane potential V(m)
  • Electrochemical driving force V(DF)

Equations

As well, we'll familiarize ourselves with two key calculations:

  • The Nernst equation
  • The Goldman-Hodgkin-Katz equation

Equilibrium Potential

Overview

Let's begin with equilibrium potential.

  • Draw a cell membrane.
  • Throughout this tutorial, we'll address the membrane potentials for sodium, potassium, chloride, and calcium.

Sodium

  • Begin with sodium.

Electrochemical Gradient of Sodium

  • Show that there is a far greater concentration of sodium ions outside of the cell than inside; a ratio of roughly 15:1.
  • Although no one knows for sure about the origins of cells, its helpful to imagine cellular life originating from seawater, growing up in salty extracellular environment.
    • For reference, seawater has a salinity of 3.5% (35 grams per liter).
  • For sodium, the intracellular concentration is ~ 10 mEq/L and the extracellular concentration is 140 mEq/L.
  • Next, balance each of the positive sodium charges with negative chloride ions.
    • The primary negative charges within neurons are chloride ions and organic anions.
  • Then, introduce our first channel: a sodium leak channel, which allows sodium ions to flow freely down their chemical gradient – from a region of high ion concentration, outside of the cell, to low ion concentration, inside of the cell.
  • Cell membranes are lipid bilayers, which are impervious to charged molecules (polar molecules), such as electrolytes (only nonpolar molecules (eg, oxygen) freely pass across the lipid bilayer). For this reason, electrolytes (which becomes ions when dissolved in water) require channels in order to cross the membrane.
  • Were it not for a separation in charge, sodium ions would fill the cell until there were even intracellular and extracellular concentrations.
  • But chloride ions cannot pass through the channel, which creates a separation in charge.
  • So, show that a positive charge forms within the cell.
  • This positive charge generates an electrostatic force directed in opposition to the chemical gradient (remember: like-charges repel one another).

Electrochemical equilibrium

  • Write that at electrochemical equilibrium, the chemical and electrical gradients are balanced.

Equilibrium potential

  • Write that the equilibrium potential, V(eq), (aka reversal potential) is the membrane potential at which an ion reaches electrochemical equilibrium.
  • We can predict the equilibrium potential by using the Nernst equation (see end of tutorial).

Membrane potential

  • Write that the membrane potential, V(m), is the voltage potential of the intracellular space in reference to the extracellular space.
  • Show that with the use of a voltmeter, we can determine the membrane potential: ; it is simply the difference between the intracellular and extracellular spaces.
  • We can predict the membrane potential by using the Goldman-Hodgkin-Katz equation (see end of tutorial).

Equilibrium potential of Sodium

  • Indicate that the equilibrium potential for sodium is + 60 mV.

Summation

  • Tying these three key concepts together, if a cell is only permeant to a single ion, then at electrochemical equilibrium, the membrane potential is equal to the equilibrium potential of that ion.
  • But cell membranes are permeant to many different ions, so the membrane potential actually relies on the equilibrium potential for many different ions, and these potentials are a part of the Goldman-Hodgkin-Katz equation.
  • Even still, potassium is far and away the most permeant ion in a neuronal membrane, so although we have to account for multiple ions to determine the membrane potential, the strongest influencer is potassium.
  • As we can see in the Goldman-Hodgkin-Katz equation, an ion's ability to permeate the membrane is a key factor in its mathematical influence on the equation. Put another way, an ion's equilibrium potential is irrelevant to the overall membrane potential, if there are too few channels for that ion to generate very much of an electrochemical gradient.
  • Thus, as it turns out, the Nernst equation calculation for the equilibrium potential of potassium is actually very near to the Goldman-Hodgkin-Katz calculation for the membrane potential of a neuron.

Potassium

Overview

  • So, now, let's take a close look at the electrochemical gradient for potassium.
  • Draw another cell membrane.
  • Include a potassium leak channel.

Electrochemical Gradient of Potassium

  • Show that (unlike sodium) there is a much greater concentration of potassium ions inside of the cell than outside; a ratio of ~ 35:1.
  • Draw an opposing electrical gradient.
  • Indicate that for neurons, potassium has an intracellular concentration of ~ 140 mEq/L and an extracellular concentration of ~ 4 mEq/L.
  • Again, balance those charges with chloride ions.

Equilibrium Potential of Potassium

  • Show that when a potassium channel opens, there is an efflux of ions out of the neuron, which creates a negative charge within the cell.
  • Draw a voltmeter and indicate that the membrane potential of potassium is - 90 mV, which, as we'll see, is similar to the neuronal membrane potential.

Neuronal Membrane Potential

Overview

Let's address the neuronal membrane potential, now.

  • We'll see how three major electrolytes (sodium, potassium, and chloride) populate the intracellular and extracellular spaces of the neuron.
  • Draw a neuron cell body.

Sodium

  • Show that sodium has a high extracellular concentration and a low intracellular concentration.
  • Indicate, that sodium enters the cell via leak channels down its concentration gradient and include the opposing electrostatic gradient.

Potassium

  • Show that potassium has a low extracellular concentration and a high intracellular concentration.
  • Show that at rest, potassium exits the cell via leak channels along its concentration gradient and include an opposing electrostatic gradient.
  • Potassium leak channels dominate the permeance of the resting neuronal cell membrane.
  • Draw a voltmeter and indicate that the resting membrane potential of a neuron is around - 70 mV. Again, very near to that of potassium.
  • Again, because potassium is the most permeant ion in a neuron, the neuron membrane potential essentially takes on the equilibrium potential of potassium.

Sodium-potassium ATPase pump

  • Now, introduce the sodium-potassium ATPase pump, which resets the ion concentrations. It maintains the resting membrane ionic concentrations and resultant membrane potential.
  • Show that it redistributes 3 sodium ions out of the cell for every 2 potassium ions it pulls back into the cell. Indicate that the sodium-potassium ATPase pump requires energy, in the form of ATP, because it is an active transporter: it performs an energy-requiring process.

Chloride

  • Lastly, let's include chloride.
  • Show that chloride has a high extracellular concentration and a low intracellular concentration; a ratio of ~ 11:1.
  • Indicate that it has a concentration gradient directed into the cell body and an opposing electrostatic gradient.
  • Chloride has an intracellular concentration of ~ 10 mEq/L and an extracellular concentration of ~ 110 mEq/L.
  • Show that chloride has an equilibrium potential of - 80 mV, which is fairly close to the membrane potential, itself, which brings us to the concept of driving force.

Electrochemical driving force

  • Write that the electrochemical driving force, V(DF), is a measure of the electromotive force on an ion. To calculate driving force, show that we subtract the equilibrium potential from the membrane potential. The greater the difference between the two potentials, the greater the driving force.
  • And write that chloride has a low driving force because the equilibrium potential for chloride is near to the neuronal membrane potential.
  • For some cells, chloride concentrations will be able to adjust themselves so the equilibrium potential will evenly match the membrane potential, and there will be no net driving force, whatsoever.

Neuronal Signaling

Synapse

  • Now, let's see learn the basic cellular physiology of neuronal signaling.
  • Let's draw a synapse, which comprises:
  • A presynaptic cell foot process (the axon terminal).
  • The postsynaptic cell dendrite (the target).
  • And the synaptic cleft between the two.
  • Draw a synaptic vesicle in the presynaptic cell and fill it with neurotransmitters, which are chemicals that provide communication between the pre- and postsynaptic cells.

Calcium channels

  • Draw a voltage-gated calcium ion channel.
  • Then, show an action potential travel down the presynaptic cell axon and depolarize the axon terminal (through sodium influx via voltage-gated sodium channels), which ultimately triggers voltage-gated calcium ion channels to open.
    • There are numerous calcium channel subtypes but its helpful to know that the N- and P/Q subtypes are the best described presynaptic high-voltage-gated calcium channels.
  • Calcium has an extracellular to intracellular concentration ratio of > 10,000:1, thus, so it has a very positive equilibrium potential: + 140 mV and a large driving force.
  • Indicate that calcium ions rush into the cell and initiates a signaling cascade wherein synaptic vesicles fuse with the presynaptic membrane and release neurotransmitter into the synaptic cleft.

Ligand-Gated Sodium Ion Channels

  • Next, draw a ligand-gated (a neurotransmitter-activated) sodium ion channel.
  • Show neurotransmitters diffuse across the synaptic cleft to a receptor on the ligand-gated ion channel, triggering it to open.
    • As we'll learn about elsewhere, glutamate is an important neurotransmitter that can bind to NMDA and AMPA receptors on these ligand-gated sodium ion channels to depolarize the postsynaptic membrane.
  • Indicate that sodium ions, then, enter the postsynaptic cell down their electrochemical gradient, which slightly depolarizes the postsynaptic membrane – makes it more positive.

Voltage-Gated Sodium Ion Channels

  • Draw voltage-gated sodium channels and show that the when the depolarization reaches a certain voltage threshold, voltage-gated sodium ion channels open.
  • Sodium rushes into the cell, which causes further depolarization in a feed-forward cycle.
  • Indicate that this positive feedback system of depolarization propagates the action potential down the postsynaptic membrane and in this manner neuronal signaling passes from one neuron to the next.

Action Potentials

Overview

  • Lastly, let's address action potentials, which are depolarization signals that operate over long distances (along an axon); they are all-or-nothing events – like firing a gun.
  • Let's create a graph.
  • Label the x-axis as time in ms.
  • Label the y-axis as membrane potential in mV.
    • Mark several specific voltages: -70 mV (the resting potential), - 55 mV (the action potential threshold), 0 mV, and + 30 mV (the peak of the action potential).

Resting Membrane Potential

  • First, indicate that at time 0, the resting state membrane potential is at -70mV.
  • Write that the voltage-gated-ion channels are closed and that potassium leak channels are the driving force. They drive the membrane potential towards the equilibrium potential of potassium.

Depolarization

  • Then, at time = 1 ms, show via a graded depolarization, the membrane potential slowly becomes less negative (it depolarizes), due to opening of ligand-gated ion channels.
  • Indicate that at -55mV, the depolarization, starts a steep climb, reflecting a rapid depolarization.
  • Mark this value as "threshold".
  • Write during depolarization, ligand-gated sodium channels open, followed by voltage-gated sodium channels, with rapid opening at threshold (-55 mv).
  • The membrane potential rapidly increases and peaks at about +30 mV, nearing towards the equilibrium potential for sodium.
    • The rapid opening of sodium channels elicits a rush of sodium influx, which is the primary driver of the spike in membrane potential.
    • This spike causes a massive depolarization, which distributes along the membrane in a self-generating, feed-forward process.
  • Voltage-gated potassium channels open more slowly sodium channels, requiring time to counter the positive sodium ion influx with an efflux of positive potassium ions.

Repolarization

  • For repolarization, show that at ~ 2 ms, the potential reverses and drops: there is increasing negativity of the membrane potential.
  • Write that repolarization reflects that at this time the sodium channels are becoming inactivated, which means that even if the membrane potential is above threshold, they cannot open: they are inactive. And the voltage-gated potassium channels are now opening.
  • Inactivation of sodium channels prevents action potentials from propagating in reverse.

Hyperpolarization

  • Show that during this time period, there is hyperpolarization of the membrane potential, because the equilibrium potential of potassium of – 90 mV, so there is net ionic driving force on potassium to leave the cell all of the way down to this potential.
  • The sodium channels are closed and the voltage-gated potassium channels remain open beyond the point where the membrane potential reaches its resting state.
  • Finally, indicate that around 4 ms after beginning of depolarization (time = 5ms), the membrane potential returns to its resting state level; at this point the voltage-gated potassium channels are closed and only the leak channels are open.

Refractory Periods

Absolute Refractory Period

  • For completeness, demarcate the absolute refractory period, which begins when the voltage reaches threshold and ends during repolarization.
    • No stimulus, no matter how strong, can cause another action potential during this period because the channels are either already open (during the depolarization) or inactivated (during repolarization).

Relative Refractory Period

  • Then, demarcate the relative refractory period, which is the time when the sodium channels are recovering from inactivation and the potassium channels remain open. It begins at the end of the absolute refractory period and it ends when the membrane potential returns to the resting potential.
  • It is possible for a stronger than normal stimulus to cause another action potential during this period but two forces oppose the possibility of depolarization: the slowly recovering sodium channels (which are coming out of inactivation) and the persistent opening of the voltage-gated potassium channels.

Antiepileptic Drug Mechanism of Action

Overview

  • Finally, as a clinical corollary, let's consider antiepileptic drugs, which are used to block the excessive or asynchronous neuronal discharges that generate seizures.

Phenobarbital and Benzodiazepines

  • First, indicate that phenobarbital and benzodiazepines accentuate chloride channel hyperpolarization. Both phenobarbital and benzodiazepines bind to the GABA-A (gamma-aminobutyric acid-A) receptor, which prolongs the opening of chloride channels.

Phenytoin and Carbamazepine

  • Then, indicate that phenytoin (Dilantin) and carbamazepine (Tegretol) bind to and prolong voltage-gated sodium channel inactivation; they lengthen the refractory period, and thus reduce the firing of fast-frequency action potentials. Oxcarbazepine (Trileptal) and Eslicarbazepine acetate (Aptiom) act in a similar manner.

Felbamate

  • Finally, indicate that one of the key roles of felbamate is that it blocks the activation of postsynaptic ligand-gated sodium ion channels; it prevents postsynaptic membrane depolarization. It, and topiramate, are NMDA receptor antagonists that block the binding of glutamate; whereas, perampanel is non-competitive inhibitor of the AMPA receptor.
  • Glutamate binds to the postsynaptic NMDA and AMPA receptors to activate the ligand-gated sodium (and calcium) ion channels.

Ethosuximide

  • Ethosuximide blocks T-type calcium channels.
  • Discussion of various calcium channel types is beyond our scope, here, but, in short: N- and P/Q type calcium channels are well established in the role that we assigned of calcium channels earlier: in the setting of axon terminal depolarization, they cause presynaptic membrane influx of calcium, which induces the fusion of synaptic vesicles to the membrane and the release neurotransmitters.
  • T-type channels, instead, are activated by small membrane depolarization (below the action potential threshold).
  • T-type calcium channels are involved in low-threshold spikes, associated with a burst-firing pattern in thalamic neurons.
  • This firing pattern is involved in sleep architecture (specifically, in thalamocortical oscillatory rhythms in Non-REM sleep) as well as of spike-and-wave discharges during absence seizures.

Valproate

  • Valproate (Depakote) causes GABA potentiation (like phenobarbital), T-type calcium channel blockade (like ethosuximide), and it blocks sodium channels (like phenytoin).

We discuss this family of drugs in more detail elsewhere.

Equations

Nernst Equation

Equation

  • V(Eq) = RT/zF * ln(Concentration(o)/Concentration(i))
    • V(Eq) = equilibrium potential
    • R = universal gas constant
    • T = temperature in Kelvin
    • z = ionic valence (Na+ = 1, Ca2+ = 2, etc...)
    • F = Faraday's constant
    • ln = natural log
    • Concentration(o) = Ion concentration in extracellular fluid
    • Concentration(i) = Ion concentration in intracellular fluid

Helpful Link

Goldman-Hodgkin-Katz equation

Equation

  • V(m) = RT/F * ln(p(Ion)Concentration(o)/p(Ion)Concentration(i))
    • Vm = membrane potential
    • R = universal gas constant
    • T = temperature in Kelvin
    • F = Faraday's constant
    • ln = natural log
    • p(Ion) = membrane permeability of an ion
    • Concentration(o) = Ion concentration in extracellular fluid
    • Concentration(i) = Ion concentration in intracellular fluid
  • Potassium, Sodium, and Chloride are all Ions in the equation, so the equation expands to:
    • V(m) = RT/F * ln(p(K+)K+(o) + p(Na+)Na+(o) + p(Cl-)Cl-(o) / p(K+)K+(i) + p(Na+)Na+(i) + p(Cl-)Cl-(i))
  • The key differences between the Goldman-Hodgkin-Katz equation and the Nernst equation, is that the Nernst equation includes the ionic valence and the Goldman-Hodgkin-Katz equation includes the membrane permeability and includes all of the ions within the cell (if they have any permeance at all).
    • Remember, because potassium's permeance far exceeds the rest, it becomes the most powerful factor in the equation and the neuronal membrane potential ends up being quite similar to the equilibrium potential for potassium.

Helpful Link