So, how do neurons convey information over long distances that results in information transfer to other neurons at synaptic connections? It is through electrical signaling that neurons are able to generate and transmit information. And this electrical signaling is possible because of a combination of…
- which in turn requires neurotransmitters, their membrane bound protein receptors and their resulting effects, including general molecular signaling within neurons as any living cell might have
* For intracellular recordings, an electrode is placed inside a cell such that the inside of the pipette is contiguous with the inside of the cell. If this electrode is connected to a voltmeter, which records transmembrane voltage across the cell membrane, one can determine the difference in voltage between the inside and outside of the cell.
* When one does this in neurons, the microelectrode reports a negative potential called the resting potential. Always a fraction of a volt (-40 to -90 mV).
* Volts are a unit of electrochemical potential energy. 1 Volt will drive 1 coulomb of charge (6.24x10<sup>18</sup> electrons) through a resistance of 1 ohm in 1 second.
To understand the basis of electrical excitability in neurons, we first need to understand that neurons, like other living cells, have a difference in electrical potential across the cell membrane when it is at rest.
To learn this physiologists stick electrodes inside of cells, including neurons. This electrode is hooked up to a voltmeter and another electrode sits outside the cell as a ground or reference electrode to complete the circuit. The difference in voltage between the inside of the cell and the outside of the cell is monitored over time and displayed on an oscilloscope.
When you do this such as with this model neuron shown here, one finds a negative resting membrane potential of the neuron with respect to the outside of approximately -70 mV.Recall that volts are a unit of electrical potential energy, where 1 Volt is defined as the amount of energy that will drive 1 coulomb of elementary charge or 6x10^18 electrons or protons through a resistance of 1 ohm in 1 second —>
And recall from physics that voltage is related to the resistance and current in an electrical circuit as described by Ohm’s law. This analogy of a water pump/water wheel circuit helps us understand these relationships better.
*Volt is defined as the difference in electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points*
: measured in amperes is the flow of electric charge across a surface at the rate of one coulomb per second. **Used to express the flow rate of electric charge**.
: So imagine the rate of water flow in this water pump as the the flow of electric charge across a cell membrane. What is the charge that is moving for a cell? Monovalent and divalent atoms like Na⁺, K⁺, Cl⁻, and Ca²⁺.
- *1A equivalent to one coulomb (roughly 6.241×10^18 times the elementary charge) per second*
- *coulomb = charge (symbol: Q or q) transported by a constant current of one ampere in one second. 1C equivalent to a charge of approximately 6.242×10^18 protons or electrons.*
- **elementary positive charge: This charge has a measured value of approximately 1.6021766208×10^−19 coulombs**
: Image the diameter of a pipe or a valve that you can regulate to be the resistance
: inverse of resistance is conducance *g* measured in siemens (S)
: for studying neuronal excitability rewriting Ohm's law as I = g(Vm-Ex) is most useful. g = conductance, no. of open channels. (Vm-Ex) = driving force causing either positive or negative current.
**Ohm’s law** from physics class relates these quantities together as V = IR, and rearranging this equation and reading it as I = V/R or Current = Voltage divided by Resistance gives you a better intuitive feel for these relations. **Notice that when you have 0 voltage or potential difference you have no current.**
: it is defined as the amount of any chemical substance that contains as many elementary entities, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of pure carbon-12 (12C).
: this number is expressed by the Avogadro constant
Action potentials are the large electrical spikes or impulses that allow neuronal signals to propagate over long distances, including nerves centimeters to meters long.
- Here is a receptor potential in a pacinian corpuscle, which is a type of mechanosensory receptor on sensory nerve endings near the surface of your skin.
- Here is an action potential in a motor neuron. **Look as the y-axes here**— the action potential has a much larger amplitude change than receptor or synaptic potentials.
To understand the basis of these electrical signals we first need to learn about how this baseline membrane potential is generated, which is the neurons membrane potential while it is at rest. We will spend most of today's class learning about the neurons resting membrane potential and which will lead into how the action potential is generated that we'll continue with next class.
I said that the resting membrane potential is more negative inside the neuron with respect to its extracellular space– this is because of the lipid bilayer and its transmembrane proteins which together make a functional cell membrane
And there is a concentration gradient in ions (which are charged atoms like sodium, potassium, and chloride) that results in this difference in distribution of charge across the neuron’s membrane
A neuron not eliciting any electrical signals is "resting" at around -70 mV. If electrical current makes the membrane voltage more positive than it is depolarizing. If it is making the membrane more negative than it is hyperpolarizing. Depolarized is less polarized. Hyperpolarized is more polarized.
Now we already saw that we can stick an electrode into a cell, and hook it up to an oscilloscope and passively record its resting membrane potential on the slide from earlier.
Then we inject a small amount of negative current (less than 1 nA) so that we hyperpolarize the cell and we see that the membrane responds passively, meaning that the membrane potential changes and recovers with an exponential relationship.
If we depolarize the cell membrane from rest by injecting pulses of positive current we get corresponding passive responses with exponential rises and decays of membrane potential–**unless that cell is a neuron and we’ve exceeded the threshold potential (shown by the red dotted line) for generating an action potential in that neuron.**
Notice if we inject stronger current pulses, we get more action potentials, also known as a higher spiking or firing rate, rather than different action potential amplitudes. If the depolarization is sufficient to generate an AP, that AP amplitude stays largely the same within each individual neuron.
All electrical signals are the due to the flow of charge, positive or negative. In this case of neurons the charge is due to the movement cations such as Na and K and anions such as Cl and neuronal membranes are selectively permeable to some of these ions giving rise to the flow of charge or current across the cell membrane.
there are active ion transporters like the Na-K ATPase and there are ion channels. For example you could pretend this is a Na channel that opens when the neuron is depolarized.
So how do ions get across the lipid cell membrane bilayer? Remember there are proteins in the cell membrane. Some of these are selective ion transporters, remember the Na-K ATPase from cell biology. These work to create concentration gradients.
There are also ion channels that form pores in the cell membrane that are selectively permeable for certain kinds of ions to cross the membrane. These allow ions move across the membrane
Here is one these ion transporters— the Na-K pump that moves 3 Na out of the cell for every 2 K in. This is an active process, requiring ATP. Moving 3 positively charged Na out for every 2 potassiums in leaving a net negative charge just across the membrane.
Ion channels span the membrane and act as pores. They can open and close, often in a voltage-dependent fashion as we will learn thursday. And ion channels even show selectively such that there are different types of Na, K channels as well as others.
And they can be additionally regulated or ‘gated’ by different mechanisms including voltage or binding of ligands such as neurotransmitters. We will learn much more about the selectivity and function of ion channels a couple lectures from now.
* Can be calculated from knowing the concentrations of ions inside and outside the cell, and the relative permeability of these ions across the cell membrane
* Nernst equation– simple formula to determine cell potentials
* Goldman equation– formula to determine resting potential when the cell membrane is permeable to more than one ion
We actually can predict what the resting membrane potential is by knowing the concentrations of ions inside and outside the cell and knowing the relative permeability of these ions to move across the cell membrane.
If a cell membrane is largely permeable to just one ion species, we can use the Nernst equation to predict the membrane potential for all kinds of cells.
<figure><figcaption class="big">orange dots K⁺, green dots Cl⁻. This simulated membrane is **only permeable to K⁺**</figcaption><img src="figs/Neuroscience5e-Fig-02.05-1R-2_163131c.png" height="500px"><figcaption>Neuroscience 5e/6e Fig. 2.5</figcaption></figure>
First let’s discuss **electrochemical** equilibrium, which is the balance of two driving forces— electrical AND chemical diffusion– across a cell membrane.
If KCl is more concentrated inside the cell, initially there is a net flux of positively charged K⁺ from inside to outside the cell due to the chemical concentration driving force which leaves the membrane hyperpolarized because of the net movement of postive charge to the outside until the this chemical force is balanced by the electrical driving force from the positively charged K⁺ being repelled by the more positive environment now outside the cell. This is called electrochemical equilibrium, and the potential at which this occurs is called the equilibrium potential for that ion.
* Initially each side of the container is neutral for charge– Every K⁺ has a Cl⁻ partner
* K⁺ diffuses down its concentration gradient since this membrane is permeable only to K⁺. Cl⁻ might want to but is not permeable. This creates a rush of K⁺ towards the other side (outside).
* After a while the positive charge builds up and the ions start to repel each other because of their like charge. This discourages more K⁺ from going out, even though its concentration difference is trying to drive it that way.
* An equilibrium will be reached which creates a net positive charge outside the cell relative to the inside. The inside (intracellular) space of the cell relative to the outside (extracellular) space is then -58 mV (for this example)
* The resting potential can be calculated using the **Nernst equation**
<div><figcaption class="big">Nernst equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.02PM_cfc06b6.png" height="100px"><figcaption>For calculations at any temperature, E<sub>x</sub> in volts (V)</figcaption></div>
Now many of the classical experiments recording membrane potential in squid axon or other preparations were conducted at room temperature, which is 20ºC or about 68ºF.
Thus to make calculations simpler in the classic scientific papers (often from the 1930s and 1940s before computers) this equation for experiments carried out at room temperature (20ºC = 68ºF = 20ºC+273ºK = 293ºK) is often simplified to the following of:
Relation of the natural logarithm (base *e* 2.718...) to the base 10 logarithm is always `ln(x) = 2.30 * log10(x)` or `ln(x) / log10(x) = 2.30`. ln() is `Math.log()` and log10() is `Math.log10()` in javascript. Copy/paste the following lines. Try varying *x* a few times and re-calculate:
* Nernst predicts linear relationship with a slope of 58 mV (58/z) per 10 fold ion change in concentration gradient <!-- .element: class="fragment fade-in"-->
Since the Nernst equation is really just a linear equation of the form y = mx, you can think of this first term at the slope and the equilibrium potential for an ion varies linearly with the log of the concentration gradient. In other words there is 58 mV per tenfold change in the concentration gradient when we are talking about our potassium examples above, which is depicted here -->
So lets imagine the following experiment we have a cell membrane, at room temperature and it is permeable only to potassium shown by the orange dots going through K⁺ ion channels. From the Nernst eqn we can calculate that the equilibrium potential for K⁺ to achieve electrochemical equilbrium in this situation is -58 mV.
That means that the chemical or concentration dependent driving force is predominant at more depolarized or more positive membrane potentials than -58mV as shown on the left here causing a net outward K⁺ flux.
At more negative membrane potentials than the nernst equilbrium potential we get net inward flow due to the stronger electrical driving force which in the case of potassium here is causing it to move against its chemical gradient.
The results of this thought experiment are displayed here, displaying the net movement of K⁺ ions into the cell when the membrane potential more negative or hyperpolarized than the K⁺ equilibrium potential, and net movement outward when the membrane potential is more positive or depolarized.
* If inside solution contains 10 mM KCl and 1 mM NaCl and outside solution contains 1 mM KCl and 10 mM NaCl...
* ...and the cell is only permeable to K⁺, equilibrium potential is -58 mV. Or if only permeable to Na⁺, than potential is +58. **Nernst eqn.**
* ...but if membrane is permeable to both K⁺ and Na⁺ (but not necessarily equally permeable) then equilibrium potential will be an intermediate value in between. Nernst cannot do this calculation.
* Requires **Goldman equation**
* The relevant ions in neurons are K⁺, Na⁺, and Cl⁻
* No sign for valence, that is why Cl⁻ is flipped
</div>
<div><figcaption class="big">Simplified Goldman equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.12PM_4416454.png" height="100px"><figcaption>For calculations at room temperature</figcaption></div>
This is all great but real cells have to deal with permeability of more than one ion species.
So imagine we have 10 mM KCl and 1mM NaCl inside the cell and 1 mM KCl and 10mM NaCl outside the cell.
If we have a simplified situation like earlier where the membrane is permeable to just K we can use Nernst eqn to show that the Veq will be -58mV at room temp. If just permeable to Na we can use Nernst to show the Veq will be +58mV
Now imagine the cell membrane is permeable to both K and Na and that these permeabilities or ability of ions to pass across the membrane are not equal for K and Na, then we have to use the Goldman eqn.
Which looks like a more complex version of the Nernst equation but with added terms that take into account the concentrations and relative membrane permeabilities of multiple ion species.
There is no valence term, thus since choride is an anion, its concentration terms are flipped.
For a typical neuron at rest, pK : pNa : pCl = 1 : 0.05 : 0.45. Note that because relative permeability values are reported, permeability values are unitless.
Table of physiological relevant intracellular and extracellular ion concentrations in squid neurons and mammalian neurons. Though the values are scaled about 4 times higher in squid, note that K is more concentrated inside, and sodium and chloride are more concentrated outside for both invertebrate and vertebrate neurons. The relevant ratios of different ion species inside and outside are similar.
* Hypothesis– if axon resting potential (-65 mV) is predominantly due to K⁺ permeability then changing [K⁺]<sub>out</sub> should change the resting potential in a manner predicted by the Nernst equation
* Experiment– stick an electrode inside axon, one outside axon (in bath). Change the concentration of K⁺ in the bath and measure new membrane potential. Assume intracellular K⁺ is unchanged during experiment.
So Hodgkin and Katz did this experiment, varying the extracellular K⁺ concentration while recording the squid axon membrane potential and found that increasing the Kout incr the resting membrane potential.
If internal K⁺ is unchanged, a plot of membrane potential against the log of external K⁺ concentration would yield a straight line with slope of 58mV per tenfold change in external K⁺ concentration at RT.
**Because other ions, particularly Cl⁻ and Na⁺, are also slightly permeable and the contribution of these other ions is more evident at low K⁺ concentrations.**
* Inside negative resting potential is due to the axon membrane being permeable to K⁺ more than any other ion
* More K⁺ inside than outside cell
* At rest K⁺ ion channels are open and allow the flow of K⁺ down its concentration gradient, this creates extra (+) ions on the outside relative to the inside and therefore a (-) resting potential
: is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Dielectric materials. Storage of electrical energy temporarily in an electric field. **Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.**
: capacitance of membrane: during change in applied voltage or current across membrane, positively charged ions pile on surface of one side of membrane and **electrostatically** interact with cations on the other side of membrane surface (membrane acts as thin impermeable surfaces in parallel, like a capacitor), repeling them and inducing immediate, fast capacitive current along membrane
<figure><figcaption class="big">Lowering Na⁺ decreases both the rate and the rise of an action potential</figcaption><img src="figs/Neuroscience5e-Fig-02.09-1R_2c02203.png" height="400px"><figcaption>
Neuroscience 5e/6e Fig. 2.9; Hodgkin and Katz *J. Physiol* 1949</figcaption></figure>
When Hodgkin and Katz did this low extracellular Na experiment, the AP had a smaller amplitude and also had a slower or longer timecourse so that the squid axon spiked at slower rate.
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## Role of sodium in the generation of an action potential
As you can see on the left here changing extracellular [Na] changes the action potential amplitude in a way largely predicted by the nernst equilbrium potential for Na, but has a negligible effect on the resting membrane potential.
* During depolarization membrane becomes super permeable to Na⁺
* There must be Na⁺ channels that are closed during rest but become open during an action potential, and closed again at the end of an action potential
And as we will soon learn, the resting membrane potential and action potential voltage is mostly due to relative changes in the permeability of the membrane to and Na vs K across the neuronal membrane. As you can see in this figure, the resting membrane potential for a neuron is close to the EK eq potential due to much greater permeability for K. During an action potential Na permeability initially increases, until the Vm approaches the ENa and then Na permeability decreases until the Vm again approaches the resting membrane potential and Pk increases.
The membrane potential rapidly depolarizes during the rising phase of an AP. Action potentials cause membrane to depolarize so much that the membrane potential transiently becomes positive with respect to the external medium, producing the overshoot. Then during repolarization, the membrane potential becomes even more negative than the resting membrane potential for a short time, giving the undershoot phase or ‘afterhyperpolarization’.
Membrane potential rapidly depolarizes Action potentials cause membrane to depolarize so much that the membrane potential transiently becomes positive with respect to the external medium, producing the overshoot. Then during repolarization, the membrane potential becomes even more negative than the resting membrane potential for a short time, giving the undershoot phase or ‘afterhyperpolarization’.
