05. Membrane Potential

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Sept., 2008

Introductory Medical Physiology


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i. Abstract

ii. Content

1. Excitable tissues

1.1 The meaning and significance of excitable tissues

1.2 Characteristics and roles of excitable tissues

1.3 Membrane potentials and ion channels

2. The intracellular and extracellular environments, and the semi-permeable

membrane

3. Concentrations, gradients, and permeability

3.1 Concentration gradients

3.2 Electrical gradients

4. Membrane potential

4.1 The meaning and significance of membrane potential

4.2 Simulation of membrane potential using a Membrane Model

4.3 Establishing resting membrane potentials

4.4 Maintaining gradients and potentials across the cell membrane

4.5 Graphical representation of membrane potentials

4.6. Calculation of equilibrium potential of ions using the Nernst equation

4.7 Calculation of membrane potential using the Goldman equation

Membrane potential exists across the plasma membrane of every cell in the body. At

rest (when not stimulated) the membrane potential reads -40 to -70 mV, reflectingunequal distribution of charges brought about by unequal ion distribution across the

plasma membrane. This phenomenon is basically due to the special characteristics of

the plasma membrane of every cell. Nevertheless, only excitable cells (neurons andmuscle cells) are able to respond to stimuli by transforming the resting membrane

potential into action potential and utilising it to carry information to the next cell. This

phenomenon is also due to a special characteristic of the excitable cells namely thepresence of gated ion channels in the plasma membrane of these cells. These ion

channels could be voltage-gated, ligand-gated, or mechanically-gated channels which

respond to voltage, chemical substances, or mechanical stimulation respectively toproduce information-carrying action potentials. The membrane potential could be

determined based on the distribution of ions across the membrane.


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iii. Checklist of topics and activities in this module

Content Page Comments on

mastery

i Abstract 4

ii Learning resources 4

iii Background knowledge 5

iv Terms to know 5

v Learning objectives 6

vi Learning activities 8

1 Excitable tissues 8

1.1 The meaning and significance of excitable tissues 8

ACTIVITY 5.1. Reception and processing of

information by cells

8

ACTIVITY 5.2: Excitable tissues 8

1.2 Characteristics and roles of excitable tissues 9ACTIVITY 5.3: Special property of excitable cells 9

ACTIVITY 5.4: Sensory receptors 9

ACTIVITY 5.5: Flow of electrical information inthe body

11

1.3 Membrane potentials and ion channels 11

ACTIVITY 5.6: Significance of membranechannels

11

2 The intracellular and extracellular

environments, and the semi-permeable

membrane

12

ACTIVITY 5.7. Movement of substances acrosscell membranes

13

ACTIVITY 5.8. Semi-permeable membrane 13

ACTIVITY 5.9: Phospholipid bilayer 14

3 Concentrations, gradients, and permeability 15

3.1 Concentration gradients 15

ACTIVITY 5.10: Diffusion of solute molecules 15

ACTIVITY 5.11: Concentration gradient and

diffusion

16

3.2 Electrical gradients 16ACTIVITY 5.12: Electrical and concentration

gradients

16

ACTIVITY 5.13: Permeability of plasmamembrane

17

4 Membrane potential 17

4.1 The meaning and significance of membrane

potential

17

ACTIVITY 5.14: Membrane potential 18


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ACTIVITY 5.15: Calculation of membrane

potential

18

4.2 Understanding membrane potential by working

with the Membrane Model

19

ACTIVITY 5.16: Simulation of membrane

potentials

19

ACTIVITY 5.17: Measuring membrane potential 21

4.3 Establishing resting membrane potentials 22

ACTIVITY 5.18: Membrane conductance 23

ACTIVITY 5.19: Equilibrium potential 24

4.4 Maintaining gradients and potentials across the

cell membrane

24

ACTIVITY 5.20: Maintaining equilibrium

potential

24

ACTIVITY 5.21: Na+ /K

+ -ATPase 25

ACTIVITY 5.22: Simulation of Na+ /K

+ -ATPase 27

4.5 Graphical representation of membrane potentials 28ACTIVITY 5.23: Graphical representation of

membrane potential

28

4.6. Calculation of equilibrium potential of ions using

the Nernst equation

30

4.7 Calculation of membrane potential using the

Goldman equation

31

vii Summary 32

ACTIVITY 2.24: Summary 32

viii Conclusion 33

ix Assessment 34

x Appendix A: Membrane template 43Appendix B: Membrane template elements 44

Appendix C: Model of voltmeter 45


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iv. Learning Resources

Please refer to the following sources for further information:

• Boron and Boulpaep, Ch. 2 & 3

• Guyton & Hall, pp 10-12 & Ch. 4

• Ganong, Ch. 1

• Marieb, Ch. 3. + Study partner

• Tortora & Grabowski, Ch. 3

• Vander, Sherman & Luciano, Ch. 3

• Supplementary materials provided

Weblinks:

http://www.lifesci.ucsb.edu/~mcdougal/neurobehavior/modules_homework/lect2.dcr

resting membrane potential

http://sky.bsd.uchicago.edu/lcy_ref/synap/resting.html Tutorial in basic neurobiology


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v. Background knowledge

Your Matriculation or STPM biology and the introductory lectures on General Anatomythat you have just had should be sufficient to get yourselves ready to enjoy going through

this module. It would also be helpful for you to review the following:

• the general structure and functions of cell membranes (Module 1).• the mechanisms of solute transport across cell membrane (Module 2).

• the definition of chemical and electrical gradients.

• the mechanism of signal transduction (Module 3).

vi. Terms to know

After studying the materials and doing the activities in this module, students should be

comfortable with the following terms:

action potentialactive transport

body fluid compartments

channelschemically activated gates

concentrationconcentration gradientsconductance

cytoplasm

depolarization

diffusiondynamic equilibrium

electrical gradients

electrodeelectrochemical gradient

electrogenic pump

fatty acid (tails)gated channels

hydrophilic

interstitial fluid (ISF)hydrophobic

ion binding sites

membrane permeabilitymembrane potentials

milliseconds (msec).Na

+ /K

+-ATPase

net charge

net movement

passive channels

phospholipid bilayerresting membrane potential

semi-permeable

solutesolvent

voltmeter

Please add other terms that you feel are relevant to your understanding of this module.


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vii. Learning objectives

Objectives from the American Physiological Society

NEU 1. Define, and identify on a diagram of a neuron, the following regions: dendrites,

axon, axon hillock, soma, and synaptic cleft.

NEU 2. Write the Nernst equation, and explain the effects of altering either the

intracellular or extracellular Na+, K

+, Cl

-, or Ca

2+ concentration on the equilibrium

potential for that ion.

NEU 3. Describe the normal distribution of Na+, K

+, Ca

2+, and Cl

- across the cell

membrane, and using the chord conductance equation, explain how the relativepermeabilities to these ions create a resting membrane potential.

NEU 4. Describe ionic basis of an action potential.

NEU 5. Contrast the generation and conduction of graded potentials with that of actionpotentials, identifying on the neuron the area in which each occurs.

NEU 6. Describe the basis for the calculation of the space constant and time constant ofneuron process.

After studying the materials in Module 5, the students should be able to:

1. Define “excitable tissue” by giving examples, by relating to its characteristics,and by stating its significance.2. Differentiate between intracellular and extracellular ionic constituents, and state

the significance of ionic imbalance across plasma membrane.3. Explain the establishment of resting membrane potential and describe how this

potential is maintained.

4. Differentiate between resting membrane potential and equilibrium potential.5. Calculate membrane potential and equilibrium potential given the appropriate

variables.

6. Relate membrane potentials to intracellular and extracellular ions and ionchannels in the membrane.

7. Represent membrane potentials in graphical forms.

Please set up more specific objectives after you have thoroughly studied the materialsin this module to help yourselves in your revision later on. Make notes that meet the

requirement of the new objectives.


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NEU 7. Define membrane capacitance and identify how membrane capacitance affects

the spread of current in myelinated and demyelinated neurons.

NEU 8. Compare conduction velocities in a compound nerve, identifying how thediameter and myelination lead to differences in conduction velocity, and the use of these

differences to classify neurons as group Ia, Ib, II, III, IV fibers or as A alpha, Abeta, Adelta, b,and c fibers.

NEU 9. Describe the ionic basis for inhibitory and excitatory post-synaptic potentials and

how these changes can alter synaptic transmission.

NEU 10. Distinguish the effects of hyperkalemia, hypercalcemia, and hypoxia on the

resting membrane and action potential.

NEU 11. Describe the effects of demyelination on action potential propagation and nerveconduction.

Neurochemistry NEU 12. Compare electrical and chemical synapses transmission based on velocity of

conduction, fidelity, and the possibility for neuromodulation (facilitation or inhibition).

NEU 13. Describe chemical neurotransmission, listing in correct temporal sequence

events beginning with the arrival of a wave of depolarization at the pre-synaptic

membrane and ending with a graded potential generated at the post-synaptic membrane.

NEU 14. Define the characteristics of a neurotransmitter.

NEU 15. Learn the synthetic pathways, inactivation mechanisms and neurochemicalanatomy and mechanisms of receptor transduction for the following neurotransmitters:

1. Catecholamines (DA, NE, E)2. Acetylcholine (ACh)

3. Serotonin (5-hydroxytryptamine; 5-HT)

4. Histamine5. GABA (gamma-aminobutyric acid)

6. Glutamate

7. Endorphins8. Enkephalins

9. Dynorphins

10. Substance P

NEU 16. Learn the major receptor classifications and representative receptor agonists and

antagonists for the above transmitters.

NEU 17. Describe the relationships between neurotransmitter dysfunction andneuropathology.


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viii. Learning Activities

1. Excitable Tissues

1.1. The meaning and significance of excitable tissues

From your previous knowledge you know that there are many types of cells in the body.

You also know that these cells are able to communicate among themselves (Module 4).You have studied the molecular mechanism of intercellular communication and we have

agreed that all cells can receive and process information. However, not all cells can

transform the information into an electrical signal to be transmitted to other cells.

Communication between adjacent cells could occur via direct contact (gap junctions, tight junctions and desmosomes) or via paracrine agents (Module 4). On the other hand,

communication between cells that are a distant apart could occur chemically via hormones

or electrically via neurons. You already have some idea now about the action of

hormones on target organs, and you’ll learn more about it in the Endocrinology course

(Semester 2). In this module, we’ll look at how some cells generate electrical signalsacross the plasma membrane and how they make use of the signals to communicate with

each other. These cells are called excitable cells.

Excitable tissues consist of cells with the ability to receive and respond to stimuli by

converting them into electrical signal. They are mainly nerve and muscle cells.

• What kinds of information do cells receive? Give examples.

• Why do cells need to be able to receive and process information?• How do cells receive and process information?

• What happens to the information eventually?

ACTIVITY 5.1: Reception and processing of information by cells

• What is the difference between excitable tissues and non-excitable tissues? Giveexamples of excitable and non-excitable tissues.

• Please explain why skeletal muscle, smooth muscle, and cardiac muscle are considered asexcitable tissues. What is the significance of muscle cells being excitable?

• What is the significance of nerve cells being excitable? Give examples to demonstrate thesignificance of nervous tissues in the body.

ACTIVITY 5.2: Excitable tissues


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1.2. Characteristics and roles of excitable tissues

All cells, excitable or non-excitable, have resting membrane potential (Section 4).

Resting membrane potential is actually the voltage difference between the inside and the

outside of the cells at rest (not stimulated). When stimulated, only excitable cells can

respond to the stimulus by generating an electrical signal called action potential. In otherwords, when stimulated, the resting potential is changed to action potential, and this can

only be carried out by excitable tissues. You will explore this phenomenon in Section 4.

What are action potentials or electrical signal impulses used for? Examples (Fig. 5.1):

• Impulses from the sensory receptors are transmitted to the central nervous systemfor perception or processing.

• Impulses are passed on from one neuron to another in the central nervous system.

• Impulses from the central nervous system are passed on to the effectors (especiallymuscles and glands) for action in response to the stimuli. Impulses that reach the

muscles and are distributed along the membranes cause the muscles to contract.

From the knowledge you gained previously in Module 3, please explain why only excitable cellscan respond to stimuli and convert them to electrical signals. Hint: presence of gated ionchannels.

The electrical signal is produced in the membrane of the excitable cells due to movement ofspecific ions across the membrane via the gated ion channel. In terms of the presence of ionchannels, what is the difference between excitable cells and non-excitable cells?

ACTIVITY 5.3: Special property of excitable cells

Some specialized excitable cells (e.g. sensory receptors) can be stimulated by specific stimulifrom the external or internal environment to produce electrical signals. Please give examplesof the sensory receptors and their external stimuli:Receptors Stimuli

Please give examples of the visceral receptors and their internal stimuli:Receptors Stimuli

In addition, a few types of cells can produce electrical signals spontaneously (no stimulusrequired). Please give an example.

ACTIVITY 5.4: Sensory receptors


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Fig. 5.1. Flow of information from the receptor to the control centre and finally to the effector

In summary, a very important characteristic that distinguishes excitable tissues from non-excitable tissues is that excitable tissues possess specific gated ion channels that would

open when stimulated, thereby allowing movements of certain ions across the membrane

to produce action potentials. What can stimulate these channels to open? Once action

potential is produced, it can be transmitted along the axon to carry a message to the targetcell. Normally, electrical signals complete a circuit between a receptor that detects

changes in internal or external environment and transmits the message to the appropriate

control centre and eventually to the effector to stabilize the change in the parameterdetected.

Receptor

Control centre

Effector

With reference to Fig. 5.1 please write a short essay on the flow of information via the neuronsand the skeletal muscle when you pick up a glass of water. Where and how is the informationinitiated? How is it passed on from one neuron to another? Where is the instruction to theeffector made? How is the instruction sent to the effector? How does the effector respond?

You can conclude that electrical signals can be transmitted from receptors to control centresand eventually to effectors for the purpose of responding to changes in external and internal

environmental parameters.

ACTIVITY 5.5: Flow of electrical information in the body


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1.3. Membrane potential and ion channels

• Membrane potential is the voltage difference between the inside and the outside of the

cells. At rest (not stimulated), it is called resting membrane potential; it does not

carry any information (why?). However, when excitable cells are stimulated by

appropriate stimuli, the resting membrane potential is converted to action potentials or impulses that are propagated along the membrane of excitable tissues (Section 4).

• Membrane potential occurs due to differential distribution of ions across the cellmembrane caused by the movement of ions in and out of the cell through specific ion

channels.

• Types of ion channels (review Module 2):i. Leakage channels (number of K+ channels >Na+ channels; this is the

reason why membrane is more permeable to K+ compared to Na+).

ii. Voltage-gated channels: participate in the generation and conduction ofaction potentials (Module 5) when stimulated by electrical stimuli.

iii. Ligand-gated or chemical-gated channels: open and close in response to

neurotransmitters, hormones and particular ions, thus establishing electricalsignals.iv. Mechanically-gated channels: open or close in response to mechanical

stimulation eg: vibration, pressure or tissue stretching, thus establishing

electrical signals.

• In which cells are each of the ion channels listed above located?

• Draw a section of plasma membrane with the four types of ion channels embedded. Usingexamples, describe the significance of these channels.

• What is “membrane potential”? Is there any movement of ions across the membrane whenthe cell is at rest (not stimulated?). Why? Is there any change in concentrations of the ionsacross the membrane at rest? Why?

• How does movement of ions across the membrane produce electrical signals?

ACTIVITY 5.6: Significance of membrane channels


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2. The intracellular and extracellular environments, and thesemi-permeable membrane

Let us assume for the moment that membrane potentials in excitable cells are produced by

the movement of ions (cations and anions) across the cell membrane (we shall verify this

in Section 4). Thus, it is important to first look at the ionic composition of theextracellular and intracellular fluids.

The chemical makeup of cytoplasm inside a cell is quite different from that of the

interstitial fluid (ISF) that bathes it (Table 5.1). It is with the ISF that cells directly

exchange molecules and ions on a continuous basis. What are some other molecules that

are exchanged?

Table 5.1. Chemical makeup of the body fluids

Substance Interstitial Fluid

Concentration (mM)

Intracellular Fluid

Concentration (mM)Na

+ 145 15

K+ 4.5 120

Ca+ 1.0 0.0001

Mg+ 1.2 58.0

Cl- 116 20

HCO3- 24 15

Phosphate ion 28 10

Glucose 4-6 0-3Amino acids 4 75Proteins 20k 160k

pH 7.4 7.0

Figure 5.2 is a simple diagram of three fluid compartments in the body (review Module

1).

• A capillary (A) is drawn to represent the blood or plasma compartment, whichexchanges water and solutes directly with the interstitial fluid compartment (C).

• The intracellular "compartment" (B) is actually the millions of individualcytoplasmic spaces inside each cell of the body. Label the compartments in Fig.

5.2.

CB

Figure 5.2. Fluid compartments of the body


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Regulation of molecular exchange between the ISF and the intracellular compartments isaccomplished by the cell membrane (Module 2). You have learnt that the cell membrane is

semi-permeable.

Fig. 5.3 represents a piece of the cell membrane with the interstitial fluid above and the

cytoplasm below. Label the compartments.

Figure 5.3. Cell membrane, solutes, and gradients

o

oo

o

o

o

o

o

o

o

o

o o

o o

o o

o

oo o

o

Intracellular

extracellular

The walls of most capillaries are quite leaky (due to gaps between endothelial cells, discussedin Module 2), and the gaps allow free exchange of water, small molecules and ions betweenthe plasma and interstitial fluid.

• In Figure 5.2, draw a small circle to represent an oxygen molecule (O2) in the blood, thenuse an arrow to indicate the direction of movement between the blood and the cell. Do thesame for CO2. Explain the forces that cause the movement of these molecules.

• Some large particles like protein molecules in the blood cannot normally cross the capillarywall, nor can most of the blood cells. Thus they are kept afloat in the vessels. What is thesignificance of this phenomenon?

ACTIVITY 5.7. Movement of substances across endothelial membranes

What is the meaning of semi-permeable membrane? Relate your answer to the structure of themembrane and the molecules that move across it.

If the smallest circleswere Na

+, what would be

their tendency in termsof movement across themembrane? Why thendoesn’t theconcentration change

with time at rest? Doyou expect other ions tobehave the same withrespect to movementacross the membrane?

ACTIVITY 5.9.Movement of ionsacross semi-permiablemembrane

ACTIVITY 5.8. Semi-permeable membrane


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Missing in Fig. 5.3 are cholesterol molecules and the large proteins that are usually shown

embedded in the plasma membranes. We will study more about these important elementslater.

3. Concentrations, gradients, and permeability

3.1. Concentration gradients

Activity 5.10 helps you to figure out the meaning and significance of concentration

gradients across plasma membrane.

Concentration gradients exist in situations where the number of molecules per unit

volume (concentration) at one location differs from that at another. In the above example,

you discovered that a concentration gradient exists across the cell membrane. The "high"end of the gradient is the location where the concentration is greatest. The other is the

"low" end. In diffusion, the net movement of molecules by random motion is down theconcentration gradient, from the high to the low end. Do molecules in a gradient ever

diffuse up the gradient?

The movement of molecules is driven by the concentration gradient that exists betweenthe two sides. A good definition of concentration gradient is "the difference in

concentration of a solute molecule over a distance between two points." One point is at the

high end of the gradient, the other point is at the low end. In this module, we will bedealing primarily with very short distances i.e. from one side of the cell membrane to the

other.

You may remember that in all fluid compartments of the body, solute molecules or ions (forexample sodium ions or glucose) are dissolved in the solvent (water). At physiologicaltemperatures, the solute particles move rapidly (Brownian motion), colliding with one another

and with the membranes of the cell. How do you relate this phenomenon to diffusion? Hint:Effect of concentration and temperature on diffusion.

Look at Figure 5.3 again. Assume for our work that the volume of solution both inside andoutside the membrane is 0.1 ml. What would be the concentration of small molecules outside inthe interstitial fluid? Use the measure "particles/ml" as the unit of measure. What are theconcentrations of medium-sized molecules both in- and outside the cell?

ACTIVITY 5.10: Diffusion of solute molecules


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3.2. Electrical gradients

Electrical gradient is the difference in total charges between the inside of the cell and theoutside of the cell. You remember that these charges are carried by the ions, and you also

remember that there is unequal distribution of ions across the membrane. Therefore, there

is an electrical gradient across the membrane.

Electrical gradients are especially important in moving charged particles into or out of a

cell. You may remember from basic principles of magnetism that like charges repel one

another, while opposite charges attract. In an electrical gradient, like that across the cellmembrane, there are more negative charges inside and positive charges outside. If the

membrane is permeable, positively charged ions (Na+, K

+ , and Ca

2+ ) will be attracted

inward, attracted to the negative charges in the cytoplasm.

Diffusion of solutes across the membrane depends on concentration and electrical

gradients, and also on membrane permeability to the solutes. Two factors that influencethe permeability of a membrane to a particular kind of solute particle are:

The direction and rate of net movement due to diffusion depends largely on the difference inconcentration for a molecule on the two sides of the membrane. The larger the difference inconcentration, the faster the rate of movement can be across the membrane. Why?

In Figure 5.3, how many concentration gradients can you identify?

If a cell membrane is permeable to solute particles, some will move across to the adjacentcompartment. In the Figure 5.3, draw some tiny solute molecules between the largerphospholipid molecules of the membrane, possibly denoting their ways from one side to theother. Add arrows to a few of the small and medium sized molecules to indicate in whatdirection you think they are heading. Explain your prediction.

Activity 5.11: Concentration gradient and diffusion

Consider the electrical and concentration gradients together (Table 5.1). Do the two gradientsfor Na

+ work in the same or opposite directions? What about K

+? Predict how you think Na

+

and K+ will move across the cell membrane. Which will have the strongest flow? Why?

Recognizing that an ion may be a part of two gradients at the same time, we can talk about itscombined electrochemical gradient. In the case of Na

+, both the chemical and electrical

gradients favour the movement of Na+ _______ the cell. However, in the case of K

+, the

chemical concentration gradient tends to move potassium ions ______________ the cell, butthe electrical gradient moves them ___________.

ACTIVITY 5.12: Electrical and concentration gradients


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a. The size of the particle. Smaller particles pass across more easily than larger

ones. Very large ones may not pass at all. The membrane is impermeable tothem.

b. The electrical charge of the particle and/or it solubility in lipids. Electrically

charged particles, called ions (example, Na+), do not dissolve well in lipids, and

the phospholipid bilayer is rather impermeable to them. The lipid connection topermeability is due to the fact that the center of the cell membrane is made of

lipids (fatty acids). Many solutes must dissolve in the lipids in order to passacross.

The movement of particles in Fig 5.3 will result in a stable distribution on either side of

the membrane for some of the particles. In this dynamic equilibrium, exchange acrossthe membrane still occurs. However, the number of particles crossing in one direction is,

over time, equal to the number crossing in the other direction, so the net movement is

zero.

In the case of large particles like carbohydrates that don't cross the membrane in Fig 5.3,

there is no dynamic equilibrium and a concentration gradient is maintained by theimpermeability of the membrane.

No electrically charged particles are shown in Fig 5.3. Based on size alone predict thepermeability of the membrane to the three types of solute particles.

If we allow diffusion to occur, starting from the arrangement of solutes shown in Fig. 5.3, predictwhat changes will occur in the distribution of particles in and outside the cell membrane.Explain your predictions.

ACTIVITY 5.13: Permeability of plasma membrane


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4. Membrane Potential

4.1. The meaning and significance of membrane potential

All cells in our bodies have membrane potentials because there is a difference in net

charge across the plasma membrane. The remainder of this module is devoted tounderstanding how membrane potential is established and maintained when the cell is at

rest. Later in Module 5, we’ll learn how membrane potential changes over time whenthere is an appropriate stimulus.

The concepts introduced here build upon your foundation of knowledge about cellmembranes and gradients. Therefore, it is essential that you have a strong grasp of the

material in the prior sections. Review if you lack confidence in understanding the earlier

material.

It is important to distinguish between charge and membrane potential. An ion carries a

positive or negative electrical charge that contributes to the net charge in one locationsuch as in the cytoplasm of a cell. The net charge is the algebraic sum of all positive and

negative charges in that area. For example if there were 5 +ve charges and 3 -ve charges,

the net charge is +2. When the net charges in two separated areas are compared there maybe a difference (gradient). The difference in charge on the two sides of the membrane isthe membrane potential.

• Based upon what you learned before, define “membrane potential” or describe what youthink a membrane potential is.

• Does a membrane potential involve a gradient? Explain.

• How does the gradient involved here differ from the concentration gradients you studiedearlier?

ACTIVITY 5.14: Membrane potential

Draw a large circle to represent a cell. Then draw:• 20 small circles with the symbol Na

+ outside the membrane and 2 inside the cell.

• 20 small circles with the symbol K+ inside the cell and 1 outside

• 16 small circles with the symbol Cl- outside the membrane and 2 inside• 5 larger circles with symbol P

- to represent proteins in the cell.

Assume the ions do not move across the membrane.

Calculate:• the gradient of each of the ion across the membrane • the net charge outside the cell • the net charge inside the cell• the difference in the net charge between the outside and the inside. This is the electrical

gradient, and it is called the membrane potential.

ACTIVITY 5.15: Calculation of membrane potential


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4.2. Simulation of membrane potential using a Membrane Model

Membrane potentials are vital to the life of every cell. They are used to produce and

conduct signals (especially in neurons and muscle cells), transport molecules across the

cell membrane (for example, in moving glucose across the wall of the gut), and many

other functions. Cells spend great amounts of energy maintaining membrane potentials by"pumping" ions in and out across the cell membrane. Understanding the cellular basis of

many physiological processes ultimately involves knowledge of membrane potentials.

Find the cell membrane template at the end of this module (Appendix A). Make a photocopyand place it on a table with the various elements that are used with it ( Appendix B).

You will notice that the membrane on the template has two gaps. In these locations you can

place a number of different elements to represent the structure of the membrane. For example,membrane "patches" simply complete the phospholipid bilayer, while channels of various typesadd functional proteins that are involved in solute transport. Finally, the molecular pumpsprovide active transport of substances across the membrane using metabolic energy (ATP).Also the template has large, negatively charged proteins shown in the cytoplasm.

In the diagram (Appendix A), what is the total negative charge of protein molecules?

Paper circles in Appendix B with plus (+) or minus (-) signs on them represent ions. For ourpurposes, we will define each ion as contributing one unit of positive or negative charge to theinside or outside of the cell. When we measure the difference in net charge on the two sides ofthe membrane, we will express the resulting membrane potential in millivolts (mV). For thissimulation each difference of one unit of charge will be recorded as a millivolt of potential. So ifthe outside has a net charge of +2 and the inside -2, the membrane potential will be -4 mV. Inactual life, each ion carries a very tiny amount of charge. Differences in the millions of ions areneeded to produce each millivolt of membrane potential.

To prepare for the simulations, cut out the elements as needed and punch out the ions using asingle-hole punch. One set will be sufficient for your group. Please do not use glue to stick theelements on the membrane model.

ACTIVITY 5.16: Simulation of membrane potentials

Fig. 5.4. Measurement of membrane potential

using a sensitive voltmeter

An "instrument" for measuring potentialdifference between the inside and outsideof the cell is the voltmeter (Appendix C).

Fig. 5.4 shows the diagram of a voltmeter

used to measure potential difference in anaxon.


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Membrane potential problem.

Cytoplasm Interstitial Fluid

Large protein (number/ total charge)

________

Large protein (number/ total charge)

________

+ve cations (number/ total charge)

________

+ve cations (number/ total charge)

___________

-ve anions (number/ total charge)

___________

-ve anions (number/ total charge)

___________

Net charge inside the cell ___________ Net charge outside the cell ___________

Membrane Potential __________________

From the above activity, you can conclude that membrane potential is determined bythe difference in net charges between the cytoplasm and the interstitial fluid.

In the model you have, the scale on the face of the meter measures between -25mV and +25mV, with zero at the midpoint. Assemble the voltmeter as directed by your instructor. Align it sothat the reference electrode is on the outside of the membrane and the recording electrode is inside. Electrodes are made of materials that conduct tiny currents to the voltmeter. With thisarrangement, the meter should display the difference between the inside charge and theoutside charge, which is the membrane potential. For example if the inside net charge was -7units and the outside net charge was +5 units, what would the membrane potential be? _______. Adjust the indicator arrow on the meter to represent this value.

Set up the voltmeter by cutting out the 2 pieces and connecting them with a paper fastener atthe center of the meter. The arrow should be set to rotate over the range of values on themeter.

• For the first exercise place membrane patches into the gaps on the template.• Next, add paper ions to the template so that the total charge outside the membrane is +8

units.• Then add ions inside the cell so that the membrane potential is -11 mV.• Record your information in the data box below. Align the arrow on the voltmeter to show

the correct reading.

ACTIVITY 5.17: Measuring membrane potential


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4.3. Establishing Resting Membrane Potentials

Although the phospholipid bilayer of the cell membrane is largely impermeable to ions

like sodium (Na+ ), potassium (K

+) and chloride (Cl

-), these ions may pass through the

membrane from time to time through passages in large protein molecules called channels

(review Module 2). With your model template you have three channels, two for Na

+

andone for K+. Channels have several important properties you should know in order to

understand transport of ions across the cell membrane:a. Channels are selective in what ions they allow to pass through them. For example,

the structure and internal electrical charges in a K+ channel enable rapid facilitated

diffusion of K+ ions to occur down the concentration gradient, but permit little or

no flow of Na+ and Cl- ions.

b. Channels may be passive or gated. Some channels, like the ones represented in this

simulation are passive; they are open all the time, allowing ions to trickle constantly

through them at some rate (for example 100 ions/sec). In Module 5 you will beconstructing gated channels that can open or close in response to changes in the

cellular environment.c. Channels can vary the conductance of the cell membrane for different ions.

Membrane conductance for a particular ion is a measure of the ease with which it can flowacross the membrane through all its channels. To understand this, set your template up withmembrane patches in both gaps. In this situation what is the Na

+conductance?

If now you substitute one Na+ channel for a membrane patch, what happens to the

conductance?

What happens if you add 2 Na+ channels?

What can you infer (in terms of channel numbers) if we say that the membrane conductance forK

+ is higher than for Na

+?

Set your template up as follows: fill the gaps with one K+ channel and one membrane patch.

Remove all ions from the ISF (outside the membrane). Add 10 K+ ions to the cytoplasm.

Record the net charge inside and outside the membrane, and the membrane potential. Setyour voltmeter to the correct reading.

Now move one K+ ion through the membrane to the outside. What happens to the net charges

inside and outside the cell? What happens to the membrane potential? What is causing the K+

ions to move outward?

Move two more K+

ions out. What happens?

You probably discovered that each time a K + ion left the cell, the inside of the cell got more

negative and the outside (ISF) got more positive . Also, the membrane potential got larger . Theresult is that a larger and larger electrical gradient is being produced with a positive end thattends to repel cations like K

+. Does the electrical gradient work with or against the outward

diffusion of K+ ions across the membrane? Will the electrical gradient inhibit the outflow of K

+?

ACTIVITY 5.18: Membrane conductance


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In the above situation where the concentration and electrical gradients oppose one another,

eventually a dynamic equilibrium would be reached. Then the number of K+ ions moving

out of the cell down the concentration gradient would exactly equal the number moving

down the electrical gradient (moving from the outside which is more positive to the inside

which is more negative). For the model, let us assume that dynamic equilibrium is reached

when 3 K

+

s have left the cell. Determine the membrane potential at that point using themodel. ________mV. This is called the equilibrium potential for K+.

In actual cells, the resting membrane potential is determined largely by the dynamic

equilibrium potential of the K+ as it has the highest conductance across the cell membrane.

Both Na+ and Cl

- have very low conductances across the membrane and influence the

membrane potential in a smaller way.

What is equilibrium potential?

If Na+ and Cl- ions had high conductance, in what direction would they move across the cellmembrane? What would be the consequence on membrane potential for each one? Pleaseexplain.

ACTIVITY 5.19: Equilibrium potential


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4.4. Maintaining gradients and potentials across the cell membrane

Your prediction is most probably right! However, we know that at rest the membrane

potential stays constant at ~-70mV, [K+] inside the cell is higher compared to outside, and

[Na

+

] outside the cell is higher compared to inside. This means that there’s a mechanismto maintain such stability of ionic composition on both sides of the membrane. Can you

suggest what this mechanism is?

Ions and molecules do regularly move against their concentration gradients across cellmembranes, but at a cost of energy to the cell. This is the process of active transport

(review Module 2).

Frame 1 of Fig 5.5 shows a diagram of a Na+ /K

+ ATPase protein embedded in the lipid

bilayer. You will notice the protein has several parts. Part B anchors it in the bilayer

because it is hydrophobic. The other sections (A, C, & D) are hydrophilic, facing into the

ISF or the cytoplasm. Segments C & D have multiple binding sites for ions. The sites withlighter outlines bind Na+, while those with heavier outlines are specific for K+. The

binding sites change shape during the transport process indicating their availability to bind

with the ions. In Frame 1, for example, the Na+

sites are open (available), while the K+

sites are closed (unavailable) to binding.

Thus far, we have discussed mostly the movement of ions down their concentration and/orelectrical gradients. Unless there were movements in the other direction (against the gradients)what do you predict would eventually happen?

ACTIVITY 5.20: Maintaining equilibrium potential

Turning to your template again, place a "pump" protein in each of the gaps in the membrane.One of the best known of these pumps is the Na

+ /K

+ -ATPase molecule (Fig 5.5). Embedded

in the cell membrane, this protein uses the energy of ATP to pump Na+ out of the cell and K

+

in, both against their gradients.

ACTIVITY 5.21: Na+ /K

+ -ATPase


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ISF

Cytoplasm

ISF

Cytoplasm

ISF

Cytoplasm

+

+++

A

B CD

EISF

Cytoplasm

+

+

+

+

++

Protein changes shape sobinding sites open for K

+

ions as Na+ ions are released

Two K+

ions attach

to open

binding sites

on the

protein

Protein changes shape so

binding sites face the ISF

again. K+ ions diffuse into

the cytoplasm. Cycle

com lete.

Na+ ions in

the

cytoplasmattach to

open

binding sites

on the

protein

pump

1 2

34

+ +

+

+

+

+

+

+

K+ ion Na+ ion

A: a hydrophilic segment of the protein pumpB: a hydrophobic segment of the protein pump

C: binding sites for Na+ ions on a hydrophilic segment of the protein pump

D: binding sites for K+ ions on a hydrophilic segment of the protein pumpE: phospholipid molecule in the membrane bilayer

Note: the energy molecule ATP and its by-products are not shown in the diagram.

Figure 5.5. Active transport across the cell membrane by the Na+/K+ ATPase protein pump

+ +


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Because of the effect the pump has on the membrane potential, it is called an electrogenic

pump. It not only restores the gradients, but also actually alters the membrane potential,

making the inside more negative compared to the outside. However, the Na+

does not

accumulate outside as it diffuses back into the cell via the leakage channel, and K+ does

not accumulate inside the cell as it diffuses out down its concentration gradient. The

balance of diffusion and active transport of K+ and Na

+ maintains the stability of the

resting membrane potential (Fig 5.6).

The ongoing work of Na+ /K

+-ATPase pumps in the cell membrane restores and maintains

the critical gradients needed to carry out other vital cell activities, especially transport andsignaling.

Fig. 5.6. The balance of diffusion and active transport of K+ and Na

+ maintains the stability of

the resting membrane potential

View the frames in Fig 5.5 to follow:a) the binding of ions (frame 2),b) the change in protein shape which exposes the binding sites to the opposite side of

the membrane (frame 3),

c) the release of Na+

ions and binding of K+

in the ISF (frames 3 & 4), andd) the completion of the cycle (back to frame 1).

To check the effects of this action on membrane potential, set up your model (Appendix A) withthe protein pumps in the gaps. Then add the following ions. Inside: 4 Na

+, 10 K

+ , 1 Cl

-; outside:

7 Na+, 3 K

+, and 3 Cl

-. Determine and record the membrane potential before the pump is

activated. _____________.

Now run a simulation, going through the steps you studied in Fig 5.5 for one cycle, moving Na+

and K+ ions across the membrane. Try to do each step. Record the new membrane potential.

In comparing your result, answer the following:a. What did the pump cycle do to the size of the gradient for each ion?

b. What did the pump cycle do for the membrane potential?

ACTIVITY 5.22: Simulation of Na+ /K

+ -ATPase


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4.5. Graphical representation of membrane potentials

Although membrane potential is actually the difference in net charges brought about bymovement of ions on both sides of cell membrane, we normally present it in graphical

form. The graph represents a recording, over time, of the membrane potential from a

single cell. You may remember that the recording electrode is inside the cell (cytoplasm)while the reference electrode is outside in the ISF (Fig. 5.4). Thus, the negative or

positive values of a membrane potential reflect the net charge inside the cell as compared

to the outside.

M e m b r a n e

o t e n t i a l ( m V )

Time (msec)

1 2 3 4 5 6 7 8 9 10

-100

-80

-60

-40

-20

0

20

12 13 14 1511

Fig. 5.7. X and Y axis for

representing membrane

potentials graphically

Examine closely the axes on Fig. 5.7. The Y-axis represents the membrane potential with theconvention we used consistently in this module. Notice especially the location of zero on the Y-axis. At zero there is no potential difference between inside and outside the cell, meaning thenet charge inside the cell is the same as the charge outside.

Going down the scale from zero, is the inside of the cell is more or less negative compared tothe outside? ___________. Is the potential difference across the membrane larger or smaller? ___________ .

Going up the scale from zero, is the inside of the cell is more or less positive compared to theoutside? ___________. Is the potential difference across the membrane larger or smaller? ___________ .

The X-axis represents time in milliseconds (msec). How many marks on the axis per msec? ________ .

Refer to Activity 5.19 and 5.22. Draw on the graph paper the membrane potential of each ofthe exercise (1-15 msec).

ACTIVITY 5.23: Graphical representation of membrane potential


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4.6. Calculation of equilibrium potential of ions using the Nernst equation

Make sure that you are very comfortable with the term “equilibrium potential”. You know

that equilibrium potential of an ion depends on :

a) intracellular concentration of the ion,

b) extracellular concentration of the ion,c) the valence (charge) of the ion.

In addition, equilibrium potential is also influenced by the temperature and the gas

constant. The relationship between the equilibrium potential of an ion to the variables is

given by the Nernst equation. Eg: for Cl-

ECl = RT ln [Clo-]

FZCl [Cli-]

Where

ECl = equilibrium potential for Cl-

R = gas constant

T = absolute temperature

F = the faraday (number of coulombs per mole of charge)ZCl = valence of Cl

-

ln = natural log

[Clo-] = Cl

- concentration outside the cell

[Clo+] = Cl

- concentration inside the cell

Converting from the natural log to the base 10 log and replacing some of the constants

with numerical values, the equation becomes:

ECl = 61.5 log [Cli-] at 37

oC

[Clo-]

Note that in converting to the simplified expression the concentration ratio is reversed

because the –1 valence of Cl- has been removed from the expression.

Similarly, for K+

EK = RT ln [Ko+] = 61.5 log [Ko

+] at 37

oC

FZK [Ki+] [Ki

+]

From the equation, notice the difference in the ratio of intracellular and extracellularcomponents between anion and the cation.


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Table 5.2 Concentration of some ions inside and outside mammalian spinal motor neurons

Ion Concentration (mmol/L of H2O) Equilibrium potential(mV)Intracell Extracell

Na+ 15.0 150.0

K+ 150.0 5.5

Cl- 9.0 125.0

Based on the values in the above table, please calculate the equilibrium potential for Cl-,

K+, and Na

+.

Suppose the membrane potential measured is –70 mV. What does it mean with regard to

the equilibrium (movement across the membrane) of the ions?

4.7. Calculation of membrane potential using the Goldman equation

The equilibrium potential for an ion is the membrane potential at which the ion on both

sides of the membrane is in equilibrium i.e. there is no net movement of the ion into or outof the cell. However, since there are more than one ion species in the ISF and in the

intacellular fluid, how is the membrane potential determined?

The magnitude of the membrane potential at any given time depends upon the

distribution of Na+, K

+, and Cl

- and the permeability of the membrane to each of these

ions. According to the Goldman equation:

EM = RT ln PK+[Ko

+] + PNa

+[Nao

+] + PCL

-[Cli

-]

F PK+[Ki

+] + PNa

+[Nai

+] + PCL

-[Clo

-]

Where:

VM = membrane potential

R = gas constant

T = absolute temperatureF = the faraday (number of coulombs per mole of charge)

PK+, PNa+, PCl- = permeabilities of the membrane to K+, Na+, and Cl-

[ ] = concentration

i = inside of the cello = outside of the cell


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vi. Summary

When we measure the membrane potential of a neuron at rest with a voltmeter by puttingone electrode inside the cell and another outside the cell, the reading says that the inside is

~70 mV more negative than the outside (by convention it is written as –70 mV). This

resting membrane potential does not carry any message to other cells, but is important as abasis for generation of graded potentials and action potentials, which are the message-carrying potentials (Modules 5 & 6). The question is: how is this resting membrane

potential established and how is it maintained?

Membrane potential results from unequal distribution of charges of the ions (mainly Na+,

K+, Cl

- and protein

-). The concentration of K

+ and protein

- is higher in the cytosol; the

concentration of Na+ and Cl

- is higher in the ISF. Since the membrane is more permeable

to K+ (there are more K+ passive channels on the membrane) than Na+, more K+ is leaving

the cell than Na+ coming in. This makes the inside of the cell more negative compared to

the outside. The electrochemical gradient is maintained by the Na+,K

+-pump.

Draw a creative and comprehensive concept map that encompasses the main ideas in thismodule.

Describe what you have learnt from this module, including non-academic outcomes.

Comment on the activities, and suggest innovations for improvement of the module.

ACTIVITY 5.24: Summary


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vii. Conclusions

Please make sure that you achieve all the objectives set up at the beginning of this module:

Objectives Comments

1. Define “excitable tissue” by givingexamples, by relating to itscharacteristics, and by stating its

significance.

2. Differentiate between intracellularand extracellular ionic constituents,

and state the significance of ionicimbalance across plasma membrane.

3. Explain the establishment of restingmembrane potential and describe

how this potential is maintained.

4. Differentiate between restingmembrane potential and equilibriumpotential.

5. Explain how resting membranepotential is maintained.

6. Calculate membrane potential andequilibrium potential given the

appropriate variables.

7. Relate membrane potentials tointracellular and extracellular ions

and ion channels in the membrane.

Don’t forget the objectives that you have constructed yourselves!


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Appendix A: Membrane template

ISF (outside cell)

Cytoplasm (inside cell)


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Appendix B : Membrane template elements

+ +

+

+

+

+

+

+

+

+

+

+

+

+ ++ +

+

+

+

+

+

+

+

++

+

+

++

+

+

+

+

+

+

++

- - - - - -

- - - - - -

Bilayer patches

Na+ Channel Proteins

Na+ /K

+ ATPase pumps

Channel gates with

receptor sitesChemical

signal

Na+ K+

Cl-

Na+ Na

+ Na

+ Na

+ K

+ K

+

K+ Channel Proteins


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Model of a voltmeter

0 +5

+10

+15

+20

+25-25

-20

-15

-10

-5

Millivolts (mV)

Carefully push the paper

fastener through the white

circle of the indicator

arrow and the black circle

of the face of the

voltmeter

05. Membrane Potential

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