membrane & action potentials module part i: a single-ion membrane potential in vitro

Membrane & Action Potentials Module

Part I: A Single-Ion Membrane Potential in vitro

Introduction

• All living cells have developed exquisite mechanisms to maintain and control an electrical potential across their plasma membranes.

• Cells use this potential to manage influx of nutrients and substrates, efflux of wastes and secreted products, regulation of cell volume, and communication between cells.

• As you will see, maintaining this potential requires a fine level of control by the cell.

Introduction (cont’d)

• This module is designed to provide a basic understanding of the factors that determine a cell’s membrane potential and a cardiac/neuronal action potential

• Though these presentations are focused on promoting a conceptual understanding, efforts will be made to explain the underlying biophysics and mathematics where appropriate.

Module Outline

• Part I. A Single-Ion Membrane Potential in vitro

• Part II. A Multi-Ion Membrane Potential in vitro

• Part III. The in vivo Membrane Potential

• Part IV. The Action Potential

Definitions

• Before we begin, let’s start with a few definitions that you should keep in mind. We’ll add to this list of definitions as we go along.

Current – the flow of charged particles (Amperes; Amps)

Potential – the separation of charge (Volts; V)

Capacitor – a non-conducting medium that allows electrostatic interaction between charges

on either side of it (Farads)

I. A Single-Ion Membrane Potential in vitro

…OK?…Let’s begin…

• As you might expect, the regulation of a membrane potential in a living cell is pretty complex.

• So, we look at the real thing, let’s start with something a little simpler. We’ll construct an apparatus that will allow us to explore membrane potentials in vitro.

• The Apparatus– One laboratory beaker – Ionic solutions

• 10mM Potassium Acetate (10mM KAc)• 100mM Potassium Acetate (100mM KAc)

– One “magic” membrane whose permeability characteristics we can control

Oh…One more thing…Instructions

• While running this module is orders of magnitude simpler than say, syncing your Outlook Calendar w/ iRocket, some brief instructions might still be valuable.– On some of the following slides you will see the commands

“(click)” and “(next)”.– When you see “(click)” an animation is on the way. Just strike the

Down Arrow or Left-Click and enjoy!– The “(next)” command means that when you strike the Down

Arrow or Left-Click you’ll be moving on to the next page.– The color of the membrane indicates the ions to which it is

permeable. For example, a red membrane means that the membrane is permeable to red ions (potassium as you’ll soon see)

• Got it? Alrighty then…happy viewing!


Beaker

Solution

Alright…Let’s start building

One beaker (click), filled with a “Solution” (click)…

(next)


Membrane…and one “special” membrane (click), which divides the solution into Solution A & Solution B.

What makes this membrane so special?

Well, as mentioned previously, we can change its permeability characteristics as we please.

(next)

Solution A Solution B


Temperature

Membrane Permeability

Solution A

Solution B

Solution A Solution B

We’ll also need a way to make note of the experimental conditions (click). The box below provides us with all the information we might need about our apparatus. Specifically, it give us the Temperature and Membrane Permeability Characteristics, as well as the compositions of Solution A & Solution B.

(next)


Temperature 298K

Membrane Permeability PK = 0 PNa = 0 PCl = 0

Solution A 10mM KAc

Solution B 10mM KAc

For example…

Here, the temperature is 298K (25°C), the membrane is Impermeable (ie not permeable) to Potassium (K), Sodium (Na) and Chloride (Cl), and both Solutions A & B are comprised of 10mM Potassium Acetate (KAc).

These conditions will be our experimental starting point.

(next)

10mM KAc 10mM KAc

A B

10mM KAc 10mM KAc

A B

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B


Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc

Recall that when in solution, an ionic salt like KAc will ionize into K+ ions and Ac- ions (click).

(next)


Finally, we’ll need a way to record the potential difference between the two solutions (click).

Notice that under these conditions the voltmeter reads “0mV”. This means that relative to the reference electrode (Solution B), the potential at the recording electrode (Solution A) is 0mV.

(next)

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc

A B

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

0mV

RecordingElectrode

ReferenceElectrode

voltmeter

0mV

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B


Now that our experimental apparatus is complete, let’s see what happens when we start making some manipulations.

0mV is boring…To get a handle on this whole membrane potential thing, let’s see if we can get that voltmeter to change its reading by altering the membrane’s permeability characteristics and/or the solution compositions in our set up.

(next)

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc


We’ll start by making the membrane permeable to potassium (click).

The membrane permeability (P) to potassium is now 1 “arbitrary unit” (PK = 1)

Notice that the voltmeter still reads 0mV.

That makes sense though, right?

(next)

0mV

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc


Although potassium ions can freely pass from A to B (click), they can also flow from B to A (click). And because the concentration of potassium ions on either side of the membrane is identical, the net flow (current) will be zero.

Thus, there will be no separation of charge, and no potential difference will develop across the membrane.

(next)

0mV

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B


Ok, let’s try changing something else.

How about changing the concentrations of the solutions?

(next)

0mV

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc

I. A Single-Ion Membrane Potential in vitroNow both solutions are 100mM KAc. But the voltmeter still reads 0mV. Why?

Well, this is essentially the same situation that we had before. While there are more potassium ions on both sides, the concentration on either side is the same.

Therefore, the NET flow will be zero (click), & no potential difference will form.

Hmm…Let’s start over.

(next)

0mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+

100mM K+

100mM Ac-

A B

100mM K+

100mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+K+

K+

K+

Temperature 298K


Solution A 100mM KAc

Solution B 100mM KAc


The previous slides suggest that in order to get a potential to develop, we’ll need the flow of ions to be unequal.

Since the concentrations of the solutions dictate flow, we’re going to need a concentration difference between the two sides (ie a concentration gradient) if we want the flow of ions to be directional. Well then, let’s establish a concentration gradient!

(next)

0mV

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B

Temperature 298K


Solution A 10mM KAc

Solution B 10mM KAc


Notice that there is now a 10-fold concentration difference across the membrane. Let’s check the voltmeter.

Hmm…still says 0mV huh? Well we know there’s a gradient now. What gives?

Whoops…permeability!

If ions cannot cross the membrane, a potential cannot develop.

(next)

0mV

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

100mM K+

100mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

K+

B

Temperature 298K



Solution B 10mM KAc

I. A Single-Ion Membrane Potential in vitroAs you’ll see below, we have the same 10-fold concentration gradient; however, the membrane is now permeable to potassium.

There are more potassium ions in Solution A than in Solution B so the NET flux of ions will be from side A to side B (click).

This leaves a net negative charge on Side A of the membrane and a net positive charge on Side B (click).

And (click)…Voila…the membrane potential is no longer 0mV.

(click)

0mV

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

Temperature 298K



Solution B 10mM KAc

An Important Note Before Moving On –In the interest of clarity, the processes of ion flux, membrane polarization, & voltmeter deflection were separated into sequential steps. In actuality they all occur simultaneously.

(next)


At this temperature (298K), the potential across the magic membrane is -59mV.

In other words, the recording electrode (Solution A) is 58mV more negative than the reference electrode (Solution B).

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

Temperature 298K



Solution B 10mM KAc


Let’s think about that a little…

Why -59mV?

Let’s start with why the potential is negative.

Well…As we said before, the net flux of potassium ions is from Solution A to Solution B. Potassium ions are positively charged. Therefore, the flow of potassium ions from Solution A to Solution B will make side A more negative than side B (next).

Temperature 298K



Solution B 10mM KAc

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

I. A Single-Ion Membrane Potential in vitroAnd what about the number 59? Why did it go to 59?

To understand this we need to consider what happens as potassium ions begin to flow across the membrane.

Recall that due to the concentration gradient, potassium will tend to flow from A to B, leaving side A more negative. This negative charge “pulls” positively charged potassium ions back toward side A.

The direction of this electrical “pull” exactly opposes the direction that the concentration gradient is “pushing” potassium.

As potassium ions continue to flow, side A becomes more & more negative and the electrical “pull” becomes greater & greater.

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++


Eventually, enough potassium ions have flowed across the membrane such that the electrical “pull” is equal to the concentration gradient’s “push”. At this point the net “force” on potassium becomes zero, and consequently the net flux of potassium ions will be zero as well.

In other words, the system has reached equilibrium.

It turns out that we could have predicted what the potential would be at equilibrium all along.

How?

By using the Nernst equation, of course!

I know…I know…”Not another equation!”Let’s try putting it into words.

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

RT [Ix]OUT

zF [Ix]IN

lnEI =


This equation states that the equilibrium potential of an ion (EI) is equal to…

the gas constant (R) times the temperature (T)…

divided by the valence of that ion (z) times Faraday’s constant (F)…

all multiplied by the natural log of the ratio between that ion’s concentration on the outside of the cell ([I]OUT) and that ion’s concentration on the inside of the cell ([I]IN).

Whew! That was a mouthful!

Ok…so maybe it wasn’t all that helpful to put it in words either.

Let’s look at where this equation comes from. That should help…

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

RT [Ix]OUT

zF [Ix]IN

lnEI =


The idea here is that equilibrium will be reached when the electrical “pull” is equal to the chemical gradient “push”.

So all we have to do is set the equation for electrical “pull” equal to the equation for chemical “push”.

Electrical “Pull” = zFE

Chemical “Push” = RT

That gives us…

Now we just solve for E…

And there you have it…The Nernst equation!

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

RT lnzFE = [Ix]OUT

[Ix]IN

ln[Ix]OUT

[Ix]IN

RT [K+]B

zF [K+]A

lnEK =


Now we’ll just make a couple of changes to make the equation applicable to our situation.

First, we’ll replace the variable “I” with “K+”

Next, instead of using “OUT” and “IN”, we’ll use “A” and “B”, recalling that when using the Nernst equation the concentration at the reference electrode (B) is always divided by the concentration at the recording electrode (A).”

Now we’ll plug everything in…

= (approx.) -59mV

…and there you go! (click)

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

(8.314)(298) 10

(1)(96500) 100lnEK =

Another Note–You might also see the Nernst equation written:

Don’t worry, it’s the same equation.

This is just a little modification that saves you the work of using those troublesome NATURAL LOGS!

(next)

RT [Ix]OUT

zF [Ix]IN

logEI = 2.3


Before we conclude our discussion of the Nernst equation though, let’s go back to that situation we had previously. You know, the one in which the membrane was permeable to potassium, but there was no potassium gradient. (click)

Now…we just said that the Nernst equation calculates the potential needed to equal the chemical gradient. Right?

Well then, what potential will be needed to balance the chemical gradient in this situation? That’s right…0mV!

So, in a sense, there’s really no difference between the situation we have here (no gradient) and when there is a gradient.

The only reason that the membrane potential doesn’t change here is because we’re starting the system at the equilibrium potential.

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

0mV

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B


Now I’m sure that there are still some burning questions that you have about this whole membrane potential thing.

Well, here are four that come up frequently. Maybe one of these is yours!

1) Why don’t the Acetate ions (Ac-) affect the membrane potential?

2) What if we considered a negatively-charged ion like Chloride (Cl-) instead of Potassium?

3) If potassium ions are flowing from side A to side B then why don’t we adjust the concentrations accordingly when we use the Nernst equation?

4) What happens if more than just potassium ions can cross the membrane?

Let’s address these one at a time.

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++

0mV

10mM K+

10mM Ac-

10mM K+

10mM Ac-

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

A B


1) Why don’t the acetate ions (Ac-) affect the membrane potential?

Good question. There is an acetate gradient across the membrane, so why don’t we consider it in the Nernst equation?

For this one, recall what happened earlier when we had a potassium gradient across the membrane, but the membrane was not permeable to potassium…Nothing.

In short, acetate ions will not affect the equilibrium potential in this case because the membrane is not permeable to acetate.

That is, if the membrane is not permeable to an ion, that ion cannot affect the membrane potential.

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++


2) What if we considered a negatively-charged ion like Chloride (Cl-) instead of Potassium?

Another Good question. If we had a Chloride (Cl-) gradient across the membrane and the membrane was permeable to Chloride the result would be very similar.

Let’s use the apparatus again to work through this…

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++


Notice that we’re all set up for a Chloride experiment…

Since we have both a Chloride ion gradient and a membrane that’s permeable to Chloride there will be a net flux of Chloride ions from A to B.

However, in this case the flow of ions leaves side A more positive, not negative.

But don’t worry, that’s not a problem…

Recall that Chloride ions are negatively charged. Therefore, as ions flow from A to B the increasingly positive side A will attract Chloride ions back.

Once again we have the electrical “pull” that’s exactly countering the chemical “push”. Equilibrium will be reached when the two are equal.

(click to see this all happen at once)

(next)

10mM NH4+

10mM Cl-

100mM NH4+

100mM Cl-

A

0mV

B

----------

++++++++++

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+

NH4+ NH4

+

NH4+

NH4+

NH4+

NH4+

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

Cl-

+59mV

I. A Single-Ion Membrane Potential in vitro3) If potassium ions are flowing from A to B then why don’t we adjust the concentrations accordingly when we use the Nernst equation?

Wow! If you came up with this one, you just might have missed your calling as a neuroscientist.

The answer involves some calculations, but the basic idea is that the number of ions flowing from A to B that are required to generate a -59mV potential is soooooo small that the effect on the original concentrations is negligible. Thus, sticking with the original concentrations in the Nernst equation is valid.

If you don’t believe me, try working out the calculation. I’ve put all the info you’ll need on the next slide.

For those of you who would prefer to skip the math, feel free to skip the next slide.

(next)

10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

----------

++++++++++


• Since running through the whole calculation here wouldn’t be any fun for either of us, I’ll just give you what you need to know in order to do it yourself, along with instructions.

1) Calculate the total capacitance of the membrane

2) Calculate the total separation of charge across the membrane for the potential and total capacitance

3) Calculate how many fundamental charges are equal to that total charge separation.

4) Compare your answer from 3) to the total number of potassium ions on either side of the membrane.

5) It’s so tiny!

• Membrane Capacitance

– 1uF/cm2 (a typical biological membrane)

• Membrane Area

– 25 cm2

• Potential (Voltage)

– -59mV

• Total Charge Separation =

(Total Capacitance) (Potential)

– Q = CV

• Fundamental Charge

– 1 x 10-19 Coulombs

• Beaker Volume

– 500mL

(next)


4) What happens if more than just potassium ions can cross the membrane?

This is an excellent question! Its solution will be the basis of our understanding of a real cell’s membrane potential.

Unfortunately though, it is beyond the scope of Part I.

Never fear though, as we will address this question directly in the sequel…

“Part II. A Multiple-Ion Membrane Potential in vitro”

(next)10mM K+

10mM Ac-

100mM K+

100mM Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+K+

K+

A

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+

K+

K+ K+

K+

-59mV

K+

Ac-

Ac-

Ac-

Ac-

Ac-

Ac-

K+

K+

K+K+

K+

K+

B

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• Before moving on to Part II though, let’s think about what we’ve learned so far.

– The minimal requirements for a membrane potential• A membrane that is permeable to at least one ion• A concentration gradient of permeant ion(s) across the membrane

– Only ions that can permeate the membrane can affect the membrane potential.

– The equilibrium potential is reached when the electrical “force” is equal to the chemical “force”.

– The Nernst equation predicts the equilibrium potential by equating the electrical and chemical “forces”.

– VERY few ions must cross the membrane in order to generate a physiologic membrane potential.

membrane & action potentials module part i: a single-ion membrane potential in vitro

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