Movement of Ions and the Cell Membrane Resting Potential

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*****Why is the resting membrane potential much closer to E(K) than E(Na)?

since the membrane at rest is more permeable to K+ than to Na+ (K+ has a relatively higher permeability/conductance than Na+ at rest), thus by the GHK and chord-conductance equations, the ionic species with the most permeability/conductance has the most influence - thus, the resting membrane potential is much closer to EK than to ENa.

If [K+]i is 100 mM and [K+]e is 10 mM, then the membrane potential at equilibrium will be x.

-61 mV

What would be the effect on membrane CONDUCTANCE? 1. Opening more ion channels 2. Opening more ion channels that allow more ions to cross per second at any particular potential.

1. increase 2. increase.

In physiological situations, the difference in concentration required to create the same resting potential increases by 10 fold for a spherical cell that is 10 times smaller in diameter. This is due to the fact that the amount of charge that moves depends on the x, while concentration changes depend on the x.

The specific capacitance of a typical cell membrane is usually very nearly x per x of membrane area (μF = microFarad).

The specific capacitance of a typical cell membrane is usually very nearly 1 μF per cm2 of membrane area (μF = microFarad).

T/F - By itself, the Nernst equation is usually not able to accurately predict the resting potential of a cell, much less the potential changes that will occur when the permeabilities of the membrane to certain ionic species change.

True

T/F - Larger cells have more membrane area and therefore a higher membrane capacitance.

True

a measure of how much charge is needed to create a given membrane potential

capacitance

If [Cl-]i is 100 mM and [Cl-]e is 10 mM, then the membrane potential at equilibrium will be x.

+61 mV

Look at the picture, why is this electroneutral?

Because the concentration of K+ and Cl- in each compartment are the same - cancelling out. Thus in I (Big K+ minus Big Cl- equals 0) In E (little K+ minus little Cl- equals 0)

By tradition, the cell x (Vm) is measured as the intracellular potential (Vi) minus the extracellular potential (Ve)

By tradition, the cell transmembrane potential (Vm) is measured as the intracellular potential (Vi) minus the extracellular potential (Ve)

Write out the chord conductance equation. What does it mean?

Current ix, through the membrane for a specific ionic species X = membrane conductance to ionic species x (gx) times the driving force (Vm - Ex)

Voltage is usually represented in equations by the symbol V or .

When a membrane has potential, how does the cell try to maintain electroneutrality?

Electroneutrality is only violated in the immediate vicinity of the membrane. Ions that cause the transmembrane potential form a 'double layer' on either side of the membrane as illustrated in Figure 2.2, with positive ions on one side of the membrane and negative ions clustering on the other side of the membrane. Everywhere else, electroneutrality holds (i.e., the number of positive and negative charges in the 'bulk solution' both intracellularly and extracellularly are equal).

***Differentiate between equilibrium potentials and membrane potentials. 1. Equilibrium potentials are specific to x and are a measure of the electrochemical energy stored by x across the membrane for that ion. The membrane potential is the x that exists across the cell membrane at any point in time, and is rarely the same as the equilibrium potential for any ion (exceptions to this are cases in which the membrane is permeable to an ion but is not x; in many cells at rest this is true of x).

Equilibrium potentials are specific to each ionic species and are a measure of the electrochemical energy stored by concentration difference across the membrane for that ion. The membrane potential is the actual potential difference that exists across the cell membrane at any point in time, and is rarely the same as the equilibrium potential for any ion (exceptions to this are cases in which the 339 Tom Shannon - Resting Membrane Potential membrane is permeable to an ion but is not actively transported; in many cells at rest this is true of chloride).

T/F - for any particular conductance, the membrane current - i.e, the net number of ions crossing the membrane per second - will be zero if Vm > EX, and will linearly increase as Vm moves away from EX.

FALSE - Note that for any particular conductance, the membrane current - i.e, the net number of ions crossing the membrane per second - will be zero if Vm = EX, and will linearly increase as Vm moves away from EX. ix = gx (Vm-Ex)

Fick's law Equation

Flux = P x A x ∆C

Saturation can be observed in ionic channels, but its importance under natural physiological circumstances is often very limited. Why?

In the first place, many ionic channels only show saturation at concentration levels of the transported ion or ions that are far larger than the concentrations that are ever encountered under natural conditions. It is also important to recognize that ionic concentrations within the body (both intracellular and extracellular) are normally maintained within a very narrow range.

It is very important to recognize that at rest many cell membranes are primarily permeable to x, but that none are exclusively permeable to this ionic species.

It is very important to recognize that at rest many cell membranes are primarily permeable to K+, but that none are exclusively permeable to this ionic species.

***By convention, positive charge leaving cell is designated positive/negative current

Note that by convention, positive charges leaving a cell (or negative charges entering the cell) are designated "positive" current.

*The Nernst Equation describes the x that will develop across the membrane on the basis of the ionic concentration difference

The Nernst Equation describes the potential that will develop across the membrane on the basis of the ionic concentration difference

If told to find the equilibrium potential for Na or K, what would you do? What does it mean?

The Nernst equation describes the electrical potential that is needed to balance the concentration gradient for a particular ionic species. This is called the equilibrium potential, and is denoted by the letter E (e.g., EK or ENa) to distinguish it from the actual membrane potential which is denoted by the letter V (Vm). Thus, the equilibrium potential for a particular ion is the potential that you get as an answer to the Nernst equation for that ion, because it will tell you the electrical potential needed to balance out the concentration gradient for a particular ionic species (the time when although concentration differences might still exist, the electrical potential balances against that)

Look at picture, which has higher capacitance?

Thinner membrane has higher capacitance.

***Equation for finding cell transmembrane potential

Vm = Vi - Ve By tradition, the cell transmembrane potential (Vm) is measured as the intracellular potential (Vi) minus the extracellular potential (Ve)

When ions diffuse, they also obey Fick's Law, but electrical forces must also be taken into account.

big idea

hyperkalemia - elevated K+ in the x?

elevated K+ concentration in the extracellular fluid.

E(K) and E(Na) (with K and Na in subscript) refers to

equilibrium potential for those particular ions.

Bulk flow

the bulk movement of solutions by hydrostatic pressure.

What two factors are considered to make up the driving force for a particular ionic species?

(Vm - Ex) Used in chord conductance equation ix (current of x) = gx(conductance to x) times the driving force (Vm - Ex)

*When we consider the movement of ions, in addition to uncharged solutes, across membranes other rules must also be considered. 1. All x uncharged solutes will eventually (in steady state) have the same concentration on both sides of the membrane (unless they are x transported). As you will see, this is not true of charged solutes even if they are not x transported (consider chloride as described below) 2. All impermeant solutes will (taken as a group) have the x concentration on both sides of the membrane (i.e. there can be no water gradients). This does NOT apply to x, or other solutes that are either impermeable, or maintained effectively impermeable due to the action of pumps or secondary active transporters. What IS required is that the total concentration of x solutes taken together be the same on both sides of the membrane. 3. x must be maintained on both sides of the membrane. This is a reasonable approximation to reality. If a membrane potential is present (as is the case across essentially all cell membranes) then there will be a small violation of electroneutrality. This is obviously necessary, since if one side of the membrane has a positive potential relative to the other side it must also have a positive charge. But the magnitude of this charge is normally extremely x relative to the bulk concentration of ions in the intracellular and extracellular fluids. For example, as will be described below, creating a resting membrane potential difference of about 60 mV across the cell membrane typically only requires that the imbalance of + and - charges on the two sides of the membrane be about 0.0001 to 0.001%. This is not detectable by normal chemical assays, and can therefore be neglected. SO THE RULE OF ELECTRICAL NEUTRALITY IS AN EXTREMELY GOOD APPROXIMATION. These are all the rules that are needed to determine cell concentrations and volumes in x situations (i.e., situations in which x and other forms of x transport are not involved). Unfortunately, such situations are rare, if, in fact, they ever occur in normal physiological situations. What is not rare is that these rules make an adequate approximation for many short-term clinical applications. These are the sorts of approximations that make such issues manageable. You should be aware of complications that arise when such approximations break-down (e.g., consequences of the failure of the Na+/K+ pump for cell volume regulation).

*When we consider the movement of ions, in addition to uncharged solutes, across membranes other rules must also be considered. 1. All permeable uncharged solutes will eventually (in steady state) have the same concentration on both sides of the membrane (unless they are actively transported). As you will see, this is not true of charged solutes even if they are not actively transported (consider chloride as described below) 2. All impermeant solutes will (taken as a group) have the same concentration on both sides of the membrane (i.e. there can be no water gradients). This does NOT apply to individual solute species - e.g., Na+ or plasma proteins, or other solutes that are either impermeable, or maintained effectively impermeable due to the action of pumps or secondary active transporters. What IS required is that the total concentration of ALL impermeant (or effectively impermeant) solutes taken together be the same on both sides of the membrane. 3. Electroneutrality must be maintained on both sides of the membrane. This is a reasonable approximation to reality. If a membrane potential is present (as is the case across essentially all cell membranes) then there will be a small violation of electroneutrality. This is obviously necessary, since if one side of the membrane has a positive potential relative to the other side it must also have a positive charge. But the magnitude of this charge is normally extremely small relative to the bulk concentration of ions in the intracellular and extracellular fluids. For example, as will be described below, creating a resting membrane potential difference of about 60 mV across the cell membrane typically only requires that the imbalance of + and - charges on the two sides of the membrane be about 0.0001 to 0.001%. This is not detectable by normal chemical assays, and can therefore be neglected. SO THE RULE OF ELECTRICAL NEUTRALITY IS AN EXTREMELY GOOD APPROXIMATION. These are all the rules that are needed to determine cell concentrations and volumes in PASSIVE situations (i.e., situations in which pumps and other forms of active transport are not involved). Unfortunately, such situations are rare, if, in fact, they ever occur in normal physiological situations. What is not rare is that these rules make an adequate approximation for many short-term clinical applications. These are the sorts of approximations that make such issues manageable. You should be aware of complications that arise when such approximations break-down (e.g., consequences of the failure of the Na+/K+ pump for cell volume regulation).

What is the equilibrium potential for Ca2+ if [Ca2+]e = 10 mM and [Ca2+]i = 1 mM? Remember that for Ca2+ the valence, z, is +2.

+30.5 mV

If you are told that an ionic species crosses a membrane and establishes a membrane potential, what two things do you need to know for calculations?

1) How large will the potential difference be? Thus you will use Nernst equation for the particular ionic species to get the equilibrium potential for that ion, giving you the electrical potential needed to balance out concentration gradient and 2) How much charge (K+) must cross the membrane to establish this potential difference? Thus, you will need to know that membrane area and membrane capacitance (typically 1 uF per cm^2 of membrane area) In simple terms, having low membrane capacitance is good for AP, high is bad. Think of membrane capacitance as how much charge likes to flow across the membrane and leak out. Thus if you remove myelin, lots will come out, membrane more permeable/higher capacitance. If you add myelin, less charge leaks out and you lower capacitance.

Name the major pumps and what they transport described for 1. Primary active transport (3) 2. Secondary active transport (cotransporters (1)/counter-transporters (2)

1. Primary active transport a. Na+/K+ ATPase - 3 Na+ out for 2 K+ in with ATP hydrolysis. Responsible for maintaining high extracellular Na+ and high intracellular K+ b. Ca2+ pump of ER and Sarcoplasmic reticulum - Sequesters Ca2+ in ER or Sarcoplasmic reticulum, but in some cells (cardiac muscle) can move Ca2+ from cytoplasm to extracellular fluid to maintain low cytoplasmic resting concentration of Ca2+ c. H+ of basolateral membrane in stomach parietal cells and kidney tubule cells. Secretion of HCl 2. Secondary Active transport a. Co-transporters Na+/glucose transporter of absorptive cells in intestinal lumen. 1 glucose into cell with 1 Na+ into the cell. Glucose moves against conc. gradient. Concentrates glucose within cell b. Counter-transporters Na+/Ca2+ exchanger - cardiac and smooth muscle membrane. 3 Na+ into cell for 1 Ca2+ out of cell. Na+/H+ exchanger

*****Major points 1. T/F - If one ionic species is much more permeable than all others, then the membrane potential will closely approach the equilibrium potential for this ion. 2. If the membrane is roughly equal in permeability (conductance) to two ions (as is frequently the case for some ionic channels and receptor/channels) then the membrane potential will roughly split the difference between the equilibrium potential for these ions. 3. When the membrane is permeable to several different ions (e.g., via different ionic channels - as is often the case in cardiac muscle), then only the actual equations can give a good approximation of the membrane potential. But reasonableness still applies: the most permeable ions have the greatest effect, but all permeable ions must be considered to arrive at accurate predictions.

1. TRUE

***What would be the effect on membrane capacitance? 1. Increasing membrane area (folding, villi) 2. Myelinating a nerve 3. Demyelinating a nerve

1. You would increase capacitance 2/3 - A thicker membrane will have less capacitance than a thinner membrane (charges farther apart).

*What is capacitance? How to understand it in simple terms?

A membrane with higher capacitance needs to have more charge to generate the same voltage. Thus, a membrane that has lower capacitance will need less current to generate the same voltage C= q/V

***At rest (i.e., when the cell membrane is at its resting potential), most cells have a relatively high permeability (conductance) to x and a much lower permeability to x. Many cells (e.g., skeletal muscle cells) also have a relatively high resting permeability to x. Note that I have used the term "relatively" because for most excitable cells the total membrane permeability to all ions at rest is much less than the total membrane permeability during all or a part of the action potential (see the following lecture).

At rest (i.e., when the cell membrane is at its resting potential), most cells have a relatively high permeability (conductance) to K+ and a much lower permeability to Na+. Many cells (e.g., skeletal muscle cells) also have a relatively high resting permeability to Cl-. Note that I have used the term "relatively" because for most excitable cells the total membrane permeability to all ions at rest is much less than the total membrane permeability during all or a part of the action potential (see the following lecture).

Look at picture, which membrane has transmembrane potential? What will happen next in the one that has the transmembrane potential?

B has potential, the separated charges generate potential and will line up on the membrane, leaving the rest of the cytosol neutral

Of Na+, K+, Cl-, and Ca2+, which has the highest conductance?

Both K+ and Cl- have the highest conductance/permeability, Ca2+ has the least. Na+ = 1 K+ = 50 Cl- = 50 Ca2+ = <0.1

*****Because it normally takes a long time for ionic concentrations to significantly change across the cell membrane, for this change to become complete could require many seconds or even a few minutes (the time depends on the membrane's permeability to x and on the x of the cell). So if the membrane potential transiently changes, then the membrane's permeability to x will try to hold the potential at its resting value. Similarly, transient increases in the membrane permeability to x will also help to hold the membrane near its resting potential (for example, thereby opposing excitatory postsynapitc inputs).

But for this change to become complete could require many seconds or even a few minutes (the time depends on the membrane's permeability to chloride and on the size of the cell). So if the membrane potential transiently changes, then the membrane's permeability to Cl- will try to hold the potential at its resting value. Similarly, transient increases in the membrane permeability to Cl- will also help to hold the membrane near its resting potential (for example, thereby opposing excitatory postsynapitc inputs).

By itself, the resting potential of a cell is often of relatively little use. However, excitable cells don't just have resting potentials. Instead, they use the ionic gradients set up by pumps and secondary active transporters to produce changes in x for such purposes as signaling and communication within an individual cell and from one cell to its neighbors. Such signals include action potentials and synaptic potentials. In addition, changes in membrane potential have become stimuli that can themselves alter the behavior of certain ionic channels; these channels (e.g., voltage- gated Na+, K+ and Ca2+ channels) can further change x and initiate complex cellular functions, such as long distance signaling via x, the initiation of synaptic transmission, the secretion of x and the initiation of contraction in muscle.

By itself, the resting potential of a cell is often of relatively little use. However, excitable cells don't just have resting potentials. Instead, they use the ionic gradients set up by pumps and secondary active transporters to produce changes in membrane potential for such purposes as signaling and communication within an individual cell and from one cell to its neighbors. Such signals include action potentials and synaptic potentials. In addition, changes in membrane potential have become stimuli that can themselves alter the behavior of certain ionic channels; these channels (e.g., voltage- gated Na+, K+ and Ca2+ channels) can further change membrane potential and initiate complex cellular functions, such as long distance signaling via action potentials, the initiation of synaptic transmission, the secretion of hormones and the initiation of contraction in muscle.

***Chloride is an ion that is (for the resting membrane) often in equilibrium across the cell membrane. This is because the membrane is X to Cl-, but this ion is not actively transported in many (or most) cells. Thus, to control Cl- effect on cell membrane potential, you need to modify its x. Chloride permeability (and changes in the membrane permeability to Cl-) can have important affects of cellular function and cell membrane potential. This is because changes in membrane potential (e.g., action potentials or synaptic potentials) are usually of relatively short duration, while the time required to change the transmembrane chloride concentration is generally much longer. So if a cell moves away from its resting potential, then chloride channels (with x roughly equaling the resting membrane potential) will 'try' to hold the membrane potential near its resting level. This is of great importance in understanding many inhibitory synapses in the CNS. It is also important in many other types of tissues (e.g., the heart).

Chloride permeability can be modified. Since ECl roughly equals resting Vm, ECl will transiently oppose any changes to the Vm because the time it takes to change the Cl- concentration gradient is much longer than the time it takes to change membrane potential via AP.

Diffusion

Diffusion results from the random thermal motion of molecules, but will result in directed (net) movement of solutes when concentration differences exist. Diffusion moves solutes from regions of higher concentration to regions of lower concentration, eventually leading to uniform concentrations (if unopposed by other processes).

Why do ionic concentration changes really screw up the T-tubule system?

Due to the small volume of the transverse tubular system and its large surface area, accumulation and depletion of ions can occur in situations that would not be significant in most tissue.

T/F - The number of ions that must cross the cell membrane to establish the resting potential can be a large fraction of the total number of ions inside and outside the cell.

False - the number of ions that must cross the cell membrane to establish the resting potential is only a very small fraction of the total number of ions inside and outside the cell.

Flux is defined as the X that moves over a specified period of time,

Flux is defined as the quantity that moves over a specified period of time,

For example, if the membrane is permeable to Na+ and K+, then it is necessary at rest that iNa + iK = x.

For example, if the membrane is permeable to Na+ and K+, then it is necessary at rest that iNa + iK = 0. No net ionic current at steady state.

This equation indicates that the most permeable ions will have the greatest effect on the transmembrane potential.

Goldman-Hodgkin-Katz (constant field) equation. GHK equation

For the chord-conductance equation, what does knowing the membrane conductance to a particular ion help you understand?

How changes in membrane potential and equilibrium potential of that ion affect the current for that particular species.

For the purposes of the exam, we should assume that Cl- is/is not actively transported

IS NOT

*****Let us consider a situation in which Cl- is NOT actively transported; in many cells this is the case, and in many others it is a good approximation. But also consider that the membrane is permeable to Cl-; further consider that the cell is at rest (no action potentials or synaptic potentials). In this situation, what will be the equilibrium potential for chloride? Why?

If the cell is at rest, the net ionic current is zero. Thus, Vm - Ek will equal 0. Thus, the equilibrium potential for chloride will be equal to the membrane potential. Why? Remember that unlike the other ionic species, Cl- is NOT actively transported. Thus, it can't build up any concentration differences on its own via active transport. Thus, chloride is adjusted to the resting membrane potential. Think of it like filling in the ECl- in the nernst equation with Vm, then calculating your extracellular Cl- and intracellular Cl- concentrations. The membrane potential will thus be your equilibrium potential, thus telling you how much extracellular/intracellular Cl- you need. Thus, the resting membrane potential is determined by other things (Na+, K+) moved by active transport, with Chloride adjusting its concentration inside and outside cell in response to changes in transmembrane potential.

In many (probably most) cells, chloride is not x (exceptions certainly exist, such as the Na-K-2Cl cotransporter that is important to the function of many epithelia, as well as some other cells, and transports Cl- against its electrochemical gradient).

In many (probably most) cells, chloride is not actively transported (exceptions certainly exist, such as the Na-K-2Cl cotransporter that is important to the function of many epithelia, as well as some other cells, and transports Cl- against its electrochemical gradient).

*****Understand that as cell (or cellular compartment) size decreases, the x of concentration changes (or imbalances in charge) increases. The most extreme example of this that we will consider is the transverse tubular system of skeletal muscle, which - due to its very small volume and large surface area - has relatively large fractions of ions cross the membrane to produce the resting potential and can experience relatively large changes in ionic concentrations as the result of a single action potential. This has important clinical consequences in certain diseases such as myotonias.

In particular, understand that as cell (or cellular compartment) size decreases, the magnitude of concentration changes (or imbalances in charge) increases. The most extreme example of this that we will consider is the transverse tubular system of skeletal muscle, which - due to its very small volume and large surface area - has relatively large fractions of ions cross the membrane to produce the resting potential and can experience relatively large changes in ionic concentrations as the result of a single action potential. This has important clinical consequences in certain diseases such as myotonias.

Why does the transverse tubular system of skeletal muscle experience relatively large changes in ionic concentrations as the result of a single action potential, whereas in most cells, the action potential does not affect the concentrations of ions greatly?

It is also important to realize that cells contain a high concentration of impermeable anions (mostly proteins and amino acids) that essentially never cross the cell membrane under normal circumstances. These are generally denoted by A-, with [A-]i ≈ x mM being typical. The interstitial fluid contains only a very small concentration of such solutes (proteins); plasma contains a larger concentration than the interstitial fluid (i.e., plasma proteins), but this is still much less than the concentration that occurs inside of cells.

It is also important to realize that cells contain a high concentration of impermeable anions (mostly proteins and amino acids) that essentially never cross the cell membrane under normal circumstances. These are generally denoted by A-, with [A-]i 344 +60 mV -95 mV -50 to -85mV +130 mV 1 50 50 < 0.1 Tom Shannon - Resting Membrane Potential ≈ 100 mM being typical The interstitial fluid contains only a very small concentration of such solutes (proteins); plasma contains a larger concentration than the interstitial fluid (i.e., plasma proteins), but this is still much less than the concentration that occurs inside of cells.

It is also worth recognizing that during a typical nerve or skeletal muscle action potential, it can be roughly estimated that the number of ions that cross the membrane (Na+ going into and K+ moving out of the cell) is typically in the range of (very roughly) 20-50 times greater than the number of ions that need to move to establish x

It is important to remember that transmembrane potentials can only be measured as the X between the intracellular and extracellular potential (e.g., with a pair of glass microelectrodes, one of which penetrates the cell membrane and the other of which is placed just outside of the cell).

It is important to remember that transmembrane potentials can only be measured as the difference between the intracellular and extracellular potential (e.g., with a pair of glass microelectrodes, one of which penetrates the cell membrane and the other of which is placed just outside of the cell).

*****K+ and Cl- are at higher concentrations in the left hand (side i) compartment than in the right hand compartment (side e). Osmotic forces are not considered in this example. However, in each compartment (e or i) the concentration of K+ and Cl- are the same - thereby preserving electroneutrality. Now consider a situation in which the membrane separating the two compartments (dashed line) abruptly becomes permeable to K+ but not to Cl-. What will happen? 1. x will flow down its concentration gradient from the left hand compartment to the right hand compartment, i.e., from side i to side e. 2. However, as K+ moves from the left to the right a net X charge will build up in the right hand compartment because there will be more positive ions (K+) there than negative ions (Cl-); remember that Cl- can not cross the membrane in this example. Similarly a net x charge builds up in the left hand compartment due to Cl- ions that are 'left behind' by the flux of K+ across the membrane. 3. Thus the right hand compartment will build up a x potential relative to the left hand compartment. This potential will x further movement of K+. ***4. Net flux of K+ will stop when the x difference (which would like to move K+ from right to left) is sufficient to just balance the x difference (which wants to move K+ from left to right). 5. Note that in the final equilibrium situation there will be an excess of x charge on side e, and an excess of x charge on side i. A x is formed at the membrane, with an excess of positive ions on the side with positive potential and an excess of negative ions on the side with negative potential. See Figure 2.2. Everywhere else the solutions are electroneutral. 6. Two obvious questions arise: 1) How large will the potential difference be? and 2) How much charge (K+) must cross the membrane to establish this potential difference? What two factors do you need to know to answer the these questions?

K+ and Cl- are at higher concentrations in the left hand (side i) compartment than in the right hand compartment (side e). Osmotic forces are not considered in this example. However, in each compartment (e or i) the concentration of K+ and Cl- are the same - thereby preserving electroneutrality. Now consider a situation in which the membrane separating the two compartments (dashed line) abruptly becomes permeable to K+ but not to Cl-. What will happen? 1. K+ will flow down its concentration gradient from the left hand compartment to the right hand compartment, i.e., from side i to side e. 2. However, as K+ moves from the left to the right a net positive charge will build up in the right hand compartment because there will be more positive ions (K+) there than negative ions (Cl-); remember that Cl- can not cross the membrane. Similarly a net negative charge builds up in the left hand compartment due to Cl- ions that are 'left behind' by the flux of K+ across the membrane. 3. Thus the right hand compartment will build up a positive potential relative to the left hand compartment. This potential will oppose further movement of K+. 4. Net flux of K+ will stop when the electrical potential difference (which would like to move K+ from right to left) is sufficient to just balance the concentration difference (which wants to move K+ from left to right). 5. Note that in the final equilibrium situation there will be an excess of positive charge on side e, and an excess of negative charge on side i. A "double layer" of ions is formed at the membrane, with an excess of positive ions on the side with positive potential and an excess of negative ions on the side with negative potential. See Figure 2.2. Everywhere else the solutions are electroneutral. 6. The answer to the first question depends on the CONCENTRATION difference for K+ on the two sides of the membrane. The answer to the second question depends of the MEMBRANE CAPACITANCE.

Look at the graph. Which membrane has a lower capacitance? What might be different between the two membranes?

Membrane 1 has a higher capacitance than membrane 2. membrane area and thickness are factors controlling membrane capacitance. C=Q/V. Thus membrane 1 has higher Q at same V, so higher capacitance

Capacitance equation (useful for understanding relationships between C, q, V

Membrane Capacitance (C) = q (charge)/V (membrane voltage) C=q/V A membrane with higher capacitance needs to have more charge to generate the same voltage. Thus, a membrane that has lower capacitance will need less current to generate the same voltage

If the Vm of a membrane is constant, what is occurring?

Membrane is at steady state if membrane potential is constant, such as resting potential. This can only occur if the SUM of all of the ionic currents is zero - no net ionic current. Thus, you could have a steady state membrane which has equal positive charge coming in for positive charge coming out.

Most of the solutes (typically about 80-90%) in both the intracellular and extracellular spaces are X.

Most of the solutes (typically about 80-90%) in both the intracellular and extracellular spaces are charged.

the x equation describes the electrical potential that is needed to balance the concentration gradient for a particular ionic species.

Nernst

*What would you expect to happen if the equilibrium potential of K+ became the same as the membrane potential?

No driving force for K+, no K+ current across membrane ix=gx(Vm-Ex)

***Name the general direction of current in these examples (Positive or negative current) 1. Na+ going out of cell 2. Na+ going into cell 3. K+ going out of cell 4. K+ going into cell 5. Cl- going out of cell 6. Cl- going into cell

Note that by convention, positive charges leaving a cell (or negative charges entering the cell) are designated "positive" current. 1. positive current 2. negative current 3. positive current 4. negative current 5. negative current 6. positive current

Note that for any particular conductance, the membrane current - i.e, the net number of ions crossing the membrane per second - will be zero if x, and will linearly increase as x.

Note that for any particular conductance, the membrane current - i.e, the net number of ions (species X) crossing the membrane per second - will be zero if Vm = Ex, and will linearly increase as Vm moves away from Ex.

One thing that the Nernst equation tells you is how far a particular ionic species is from xequilibrium. It is also very useful in seeing why changes in the concentrations of various ions have particular effects on the membrane potential (e.g., hyperkalemia - which is elevated K+ concentration in the extracellular fluid).

One thing that the Nernst equation tells you is how far a particular ionic species is from electrochemical equilibrium. It is also very useful in seeing why changes in the concentrations of various ions have particular effects on the membrane potential (e.g., hyperkalemia - which is elevated K+ concentration in the extracellular fluid).

In a situation where 2 ionic species have essentially comparable conductances (permeabilities), what will the membrane potential be?

Remember that the GHK and chord conductance equations tell us that the ionic species with highest permeability (conductance) has the biggest effect on membrane potential. Thus, if 2 ionic species have the same conductance, the membrane potential will adjust to halfway in between the equilibrium potentials of the ionic species involved. Thus, if conductance of Na and K is the same, the membrane potential will adjust to halfway between their equilibrium potentials

Similar to what the GHK equation tells us about permeability of ions influencing their effect, the chord-conductance equation tells us that the ionic species with the largest x has the greatest effect on the membrane

Similar to what the GHK equation tells us about permeability of ions influencing their effect, the chord-conductance equation tells us that the ionic species with the largest conductance has the greatest effect on the membrane

For example, if the membrane is permeable to Na+ and K+, then it is necessary at rest that iNa + iK = 0. So, gNa(Vm-ENa) + gK(Vm-EK) = ?.

So, gNa(Vm-ENa) + gK(Vm-EK) = 0.

This is called the equilibrium potential, and is denoted by the letter E (e.g., EK or ENa) to distinguish it from the actual membrane potential which is denoted by the letter V (Vm). What does the equilibrium potential represent?

The cell membrane resting potential is simply the X across the cell membrane that occurs when the cell is at rest - i.e., when it is not involved in transmembrane potential changes such as synaptic potentials or action potentials.

The cell membrane resting potential is simply the difference in potential across the cell membrane that occurs when the cell is at rest - i.e., when it is not involved in transmembrane potential changes such as synaptic potentials or action potentials.

In the chord-conductance equation, what does the conductance of a membrane refer to? What is it in simple terms?

The conductance of the membrane to any given ionic species is simply a measure of how easily this ion can cross the membrane. Thus it is essentially analogous to the membrane permeability for this ionic species (there are differences, but you don't have to worry about them in this course).

The X of the membrane to any given ionic species is simply a measure of how easily this ion can cross the membrane. Thus it is essentially analogous to the membrane permeability for this ionic species (there are differences, but you don't have to worry about them in this course).

The conductance of the membrane to any given ionic species is simply a measure of how easily this ion can cross the membrane. Thus it is essentially analogous to the X for this ionic species (there are differences, but you don't have to worry about them in this course).

The fact that cells have resting potentials is due to gradients of ions established by 'x, as well as x molecules, that produce concentration gradients for various ions - most importantly Na+ and K+. As you will see shortly, such concentration differences, combined with the x of the membrane to certain ions (i.e., varying numbers of open ionic channels of different types) are the cause of the resting membrane potential. In addition, changes in the x to various ionic species are the cause of changes in membrane potential.

The fact that cells have resting potentials is due to gradients of ions established by 'pumps' (or ATPases), as well as secondary active transport molecules, that produce concentration gradients for various ions - most importantly Na+ and K+. As you will see shortly, such concentration differences, combined with the selective permeability of the membrane to certain ions (i.e., varying numbers of open ionic channels of different types) are the cause of the resting membrane potential. In addition, changes in the membrane permeability to various ionic species are the cause of changes in membrane potential.

The resting potential of various cells within the human body ranges from as little as about x mV to as much as about x mV. Cardiac and skeletal muscle cells generally have resting potentials of about x mV. Nerve cells usually have somewhat smaller resting potentials in the neighborhood of x mV.

The resting potential of various cells within the human body ranges from as little as about -10 mV to as much as about -90 mV. Cardiac and skeletal muscle cells generally have resting potentials of about -90 mV. Nerve cells usually have somewhat smaller resting potentials in the neighborhood of -70 mV.

wo equations are in common usage to give approximations to what can be expected when the membrane is permeable to multiple ionic species. These are the x equation (also called the x equation) and the x equation.

These are the Goldman-Hodgkin-Katz (GHK) equation (also called the constant field equation) and the chord conductance equation.

All impermeant solutes will (taken as a group) have the same concentration on both sides of the membrane (i.e. there can be no water gradients). When does this rule not apply?

This does NOT apply to individual solute species - e.g., Na+ or plasma proteins, or other solutes that are either impermeable, or maintained effectively impermeable due to the action of pumps or secondary active transporters. What IS required is that the total concentration of ALL impermeant (or effectively impermeant) solutes taken together be the same on both sides of the membrane. In passive situations

T/F - The relationship between membrane potential and charge is simple and it is linear.

True - For any given membrane, the more charge that crosses the membrane, the larger will be the resulting potential difference. C = Q/V Membrane has constant capacitance, thus V will increase as Q increases

The electrochemical potential difference for an ionic species is also known as this, and does this major function

Vm - EX is referred to as the driving force, (also called the electrochemical potential difference, or EPD) since it is this potential difference that drives the particular ionic species across the membrane through open ionic channels.

Vm - Ex is referred to as the driving force, (also called the electrochemical potential difference, or EPD) since it is this potential difference that drives the particular ionic species across the membrane through x.

it is this potential difference that drives the particular ionic species across the membrane through open ionic channels.

Voltage is a measure of the amount of X it takes to X two groups of charges.

Voltage is a measure of the amount of work it takes to separate two groups of charges.

Voltage is a measure of the amount of work it takes to separate two groups of charges. Normal solution is electroneutral and it takes energy to separate charges in solution. In physiology, this separation is normally maintained by a membrane which stretches between groups of charged ions. If the membrane is made slightly permeable to one or more of these ions, they will flow across the membrane in an effort to join their opposites on the other side. This flow is measured as X and it is proportional to the X.

*****When the membrane is simultaneously permeable to more than one ionic species, a steady state situation (i.e., a situation in which the x is constant - such as the resting potential) can only occur if the x.

When the membrane is simultaneously permeable to more than one ionic species, a steady state situation (i.e., a situation in which the membrane potential is constant - such as the resting potential) can only occur if the sum of all of the ionic currents is zero (i.e., there is no net ionic current).

What is steady state for a membrane?

***When we talk about voltage in this class we will actually be talking about the X between two points. That is, we talk about the voltage at one point relative to a reference voltage at another point. Physiologically this usually means the voltage X the cell membrane relative to the voltage X the membrane (by convention). It is also termed the "potential difference". Simply put, you can think of the membrane potential difference as a measure of how much ions "want" to move either into or out of the cell because of their charge.

When we talk about voltage in this class we will actually be talking about the difference in voltage (ΔV) between two points. That is, we talk about the voltage at one point relative to a reference voltage at another point. Physiologically this usually means the voltage inside the cell membrane relative to the voltage outside the membrane (by convention). It is also termed the "potential difference". Simply put, you can think of the membrane potential difference as a measure of how much ions "want" to move either into or out of the cell because of their charge.

Fick's Law basically describes the flux across a membrane of a solute from diffusion in terms of X (P), the X (A), and the X (ΔC) across the membrane.

basically describes the flux across a membrane of a solute from diffusion in terms of permeability (P), the membrane area (A), and the concentration difference (ΔC) across the membrane. Flux = P x A x ∆C

Another equation that describes the membrane potential when several ionic species are permeable is called the "Chord Conductance Equation". But to understand this equation, you need to be able to incorporate x into your equation

conductance

T/F - Smaller cells have less membrane area and therefore a higher membrane capacitance.

false More membrane area = higher capacitance Increased membrane thickness = decreased capacitance

T/F - the Nernst equation always describes the actual membrane potential

false - it is rarely (if ever) the case that a cell membrane is only permeable to one species of ions. Instead, the Nernst equation describes the electrical potential that is needed to balance the concentration gradient for a particular ionic species.

Serum potassium is normally about 4 mM, and is usually tightly controlled. When extracellular K+ too low, you get x, when too high, you get x. Both situations are caused especially by x malfunctions. Hyperkalemia is considered to exist if K+ extracellular is greater than x mM, and is considered moderate when K+ extracellular is in the range of x to x mM. If K+ extracellular exceeds x mM than hyperkalemia is considered severe and life threatening, due to cardiac arrhythmia and possible cardiac arrest. You see changes in the ECG pattern. ***With the normal K+ concentrations extracellularly listed as 4 mM, if K+ extracellular increases to 8 mM, what will happen to equilibrium potential of K? How will this affect the Vm? How would you treat hyperkalemia and why?

hypokalemia = too low extracellular K+ hyperkalemia = too high extracellular K+ resting extracellular K+ = 4 mM hyperkalemia = 5 mM Moderate = 6.5 to 8 mM Severe = 8mM - 12 mM Deadly = 12 mM above If K+ extracellular increases to 8 mM, the equilibrium potential will become less negative (about 20 mV more positive), and the resting potential will also increase. Treat by administering IV with saline to dilute the K+, with glucose to promote insulin production that drives K+ entry into cells, and bicarbonate to promote alkalinization that also promotes K+ entry into cells.

If the permeabilities to Na+ and Cl- are zero, then the GHK equation reduces to the Nernst equation for K+. Similarly, if the permeability of the membrane to K+ is much greater than that for Na+ and Cl-, then the equation indicates that the membrane potential will be very near the x.

if the permeabilities to Na+ and Cl- are zero, then the GHK equation reduces to the Nernst equation for K+. Similarly, if the permeability of the membrane to K+ is much greater than that for Na+ and Cl-, then the equation indicates that the membrane potential will be very near the equilibrium potential for K+.

Typically, are impermeable anions (mostly proteins and amino acids) more prevalent in interstitial fluid or inside the cell?

inside the cell. The interstitial fluid contains only a very small concentration of such solutes (proteins); plasma contains a larger concentration than the interstitial fluid (i.e., plasma proteins), but this is still much less than the concentration that occurs inside of cells.

competition is usually not of much importance to ionic channels under normal physiological conditions, mostly because

ionic concentrations in the body do not vary over wide ranges.

Myelination is simply like having a very thick membrane, i.e., capacitance is reduced and therefore less/more charge is needed to change the membrane potential

less

At rest (i.e., when the cell membrane is at its resting potential), is the general permeability (conductance) relatively high or low for Na+, K+, Cl-?

most cells have a relatively high permeability (conductance) to K+ and a much lower permeability to Na+. Many cells (e.g., skeletal muscle cells) also have a relatively high resting permeability to Cl-. Note that I have used the term "relatively" because for most excitable cells the total membrane permeability to all ions at rest is much less than the total membrane permeability during all or a part of the action potential (see the following lecture)

myelin effectively increases membrane thickness and thereby x membrane capacitance.

myelin effectively increases membrane thickness and thereby reduces membrane capacitance.

On its own, the Na+/K+ ATPase would generate a positive/negative current.

positive - more + charge leaving the cell, positive current

t is also important to realize that (like several other active transport molecules) the Na+/ K+ pump is x in nature. This results from the fact that the Na+/K+ pump moves 3 Na+ ions out of the cell and 2 K+ ions into the cell for every molecule of ATP that is split.

t is also important to realize that (like several other active transport molecules) the Na+/ K+ pump is electrogenic in nature. This results from the fact that the Na+/K+ pump moves 3 Na+ ions out of the cell and 2 K+ ions into the cell for every molecule of ATP that is split.

the Na+/K+ pump typically only contributes x mV or less to the resting membrane potential.

the Na+/K+ pump typically only contributes 10 mV or less to the resting membrane potential.

The Nernst Equation describes the potential that will develop across the membrane on the basis of the x difference

the Nernst Equation describes the potential that will develop across the membrane on the basis of the ionic concentration difference

The Nernst equation describes the x that is needed to balance the x for a particular ionic species.

the Nernst equation describes the electrical potential that is needed to balance the concentration gradient for a particular ionic species.

T/F - A thicker membrane will have less capacitance than a thinner membrane.

true

T/F - Even without the restorative power of the Na+/K+ pump, several hundred action potentials could fire without greatly changing ionic concentrations

true

T/F - If a membrane potential is present, then there will be a small violation of electroneutrality

true

T/F - In real life, extracellular Cl- is usually much greater than intracellular Cl-

true

T/F - Smaller cells (or regions of cells) require larger concentration differences to establish the same potential difference

true

T/F - The most permeable ions will have the greatest effect on the transmembrane potential.

true

T/F - There is a net movement of charge during every cycle of the Na+/K+ ATPase (one positive ion out of the cell). This produces a potential difference that contributes to the cell membrane resting potential.

true

T/F - The Na+/K+ ATPase generates a potential difference in its action, but this contribution to the resting membrane potential is small

Movement of Ions and the Cell Membrane Resting Potential

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