True or false: When ions diffuse, they obey Fick's law, but electrical forces must also be taken into account.
What are the rules concerning the movement of ions and uncharged solutes?
a. all permeable uncharged solutes will eventually have equal concentrations on both sides unless they are actively transported. this is not true for charged solutes, such as chloride
b. all impermeant solues as a group will have the same concentration on both sides of the membrane. does not apply to individual solutes (Na+, plasma proteins) or solutes maintained effectively impermeable due to action of pumps or sec active transporters. What is required is that total concentration of ALL impermeant (or effectively impermeant) solutes taken together are the same on both sides of the membrane (cell membranes cannot stand water gradient)
c. electroneutrality must be maintained on both sides of the membrane. is an approximation but is a reasonable one. to have membrane potential, must have more positive ions on one side of membrane than the other but the magnitude of the difference in charge is normally extremely small relative to bulk concentration of ions in the intracelluar and extracellular fluids. for example, when creating resting membrane potential difference of about 60mV accorse cell membrane, it typically only requires that the imbalance of + and _ charges be about 0.0001 to 0.001%
Note: these are all rules needed to determine cell concentrations and volumes in passive situations (no pumps or other forms of active transport involved) which is not reality. However, these rules make adequate approximation for short-term clincal applications
Discuss the definition of voltage and how it relates to electrical current.
Voltage is a measurement of the amount of work it takes to separate 2 groups of charges. Normal solution is electroneutral and it takes energy to separate charges in solution. In body systems, spearation of charge is maintained by a plasma membrane. If membrane is made slightly permeabl to one or more ions, they will flow across the membrane to join opposite charges on the other side. This flow is measured as electrical current and is proportional to voltage.
What is resting membrane potential? How is it calculated? How is resting membrane potential established and why is this important?
Difference in potential across a cell membrane that occurs when cell is at rest i.e. not involved in transmembrane potential charges such as synaptic potentials or action potentials
Cells have resting potentials due to gradients of ions established by pumps/ATPases and secondary active transport. resting membrane potential is of little use, however, cells use the ionic gradients set by pumps and sec active transporters to produce changes in membrane potential for signaling and communication
Imagine a concentration cell with KCl on both sides with a higher concentration intracellularly. What would happen if K+ was made permeable but not Cl-? How large will the potential difference be and how much charge (K+) must corss the membrane to establish the potential difference?
1. K will flow down its concentration gradient from inside to outside of the cell. However, this will cause a net positive charge to build up extracellulary bc there will be more K+ ions than Cl- ions. This positive potential will oppose the further movement of K+ and net flux of K+ will stop when the electrical potential difference balances the concentration difference. At equilibrium, there will be an excess of + charge extracellulary and a "double layer" of ions will form at the membrane with an excess of positive ions lined up against the membrane and negative ions lined up agains the membrane intracellularly. Everywhere else, the solutions are electroneutral.
2. The potential difference depends on the concentration difference for K+ on both sides of on both sides of the membrane. If you have a large concentration difference, need more voltage to stop ion flux. When have smaller concentration difference, don't need as much voltage to inhibit ion flux. How much K+ needs to cross the membrane to establish potential difference depends on capacitance.
What is the Nernst equation? What is it used for?
the Nernst equation describes the potential that will develop across a membrane on the basis of the ionic concentration difference where ONE ion is permeable. In real life, have more than one ion permeable and all compete to reach their membrane potentials. It describes the electrical potential needed to balance the concentration gradient for a particular ionic species (which is the equilibrium potential, EK for example). In other words, it is the potential at which the concentration and charge gradients of ion are equal and opposite. Can tell you how far away a particular ion species is from chemical equilibrium as well as why changes in concentrations of various ions have particular effects on membrane potential (e.g. hyperkalemia)
What is capacitance? What factors determine the capacitance of a cell?
1. capacitance is the amount of charge needed to establish a certain membrane potential (C=Q/V). The higher the capacitance, the more charge needed to cross the membrane to establish a particular voltage which means it is harder to generate an action potential (AP)
2. Capacitance increases with membrane area and membrane capacitance is generally linearly related to membrane area. (more membrane, need more charge per sq cm to acheive certain voltage).
A thicker membrane will have less capacitance than a thinner membrane
What is the difference btwn equlibrium potential and membrane potential?
equilibrium potential: measure of electrochemical energy stored by concentration difference across a membrane for a specific ion
membrane potential: the actual potential difference across a cell membrane at any point in time (is rarely the same as equilbrium potential for any ion except for ions that are not actively transported such as Cl-)
As the size of a cell or cellular compartment decreases, the magnitude of concentration changes (or imbalances in charge) increases. Discuss an example of this in the body and why this is important.
The most extreme example we will consider is the T-tubule 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 relativley large chnages in ionic concentrations as the result of a single action potential. Has clinical importance in diseases such as myotonias.
What is the Goldman-Hodgkin-Katz (GHK)/constant field equation and how is it useful?
because the Nernst equation looks at Vm (resting potential) when only one ion is permeable (and this is not realistic) the GHK equation is an approxmation that can be used to determine Vm when more ions are permeable (K+, Na+, Cl-). Vm is dependent on the ion permeability. In the equation, if for example, you make the permeabilities for Na+ and Cl- 0, the equation is reduced to the Nernst equation for K+. Therefore, the most permeable ions will have the greatest effect on transmembrane potential. The Na+/K+ ATPase causes increased permeability of K+ and accounts for 10 mV of Vm (in example given on slide 9 of notes, Vm is closer to the equilibrium potential for K+ because it is more permeable)
see pg 66 of course notes for equation
True or false: Smaller cells require larger concentration differences to establish the same potential difference as a large cell. Explain your answer.
True. This is due to the fact that the amount of charge that moves (capacitance) depends on surface area, while concentration depends on volume. In T-tubules of skeletal muscle, diameter is 0.1-0.2 micrometers (larger in cardiac muscle). So to establish the normal resting potential near -90 mV, an increase of K+ in the T-system of as much as 0.2% may have to take place. Is still very small fraction of total available K+ but is far more significant than would occur in larger cells (or cellular regions). (Small volume=less space to fit enough charge to effect Vm). Due to the small volume of the T-tubule system and its large surface area, accumulation and depletion of ions can occur in situations that would not be significant in most tissues.
Although T-tubules are continuous with ECM, it is by an exceedingly narrow and tortuous pathway. The long and convoluted pathway means diffusion can required a relatively long time to return concentrations to their original values following an action potential.
What is the chord conductance equation and why is it useful? Be sure to include a discussion of current and driving force.
firstly, remember that conductance is essentially a measure of permeability of an ion through a membrane. If you increase the open probability of an ionic channel than conductance is higher. Also, open ion channels that allow more ions to cross per second at any particular potential also mean a higher membrane conductance. Membrane conductance is denoted for a particular ionic species by gx . The current, ix, through the membrane is defined by the Chord conductance equation:
Vm is membrane potential and Ex is equilibrium potential. *Note: positive current=positive charges leaving a cell or negative charges entering a cell
Vm-Ex is the driving force, aka the electrochemical potential difference (EPD) since it is this potential difference that drives the ionic species across the membrane. If Vm=Ex, membrane current i.e. net ion flux is 0 and increases linearly as Vm moves away from Ex
When the membrane is permeable to more than one ionic species, a steady state situation (constant Vm, resting membrane potential) can only occur if the sum of all of the ionic currents is 0. If not, then ionic current would be constantly changing membrane potential. see pg 68 of course notes for equation calculating Vm with multiple permeable ions. Also see pg 9 of PPT
Take home message: The ionic species with the largest conductance has the greatest effect on membrane potential. If 2 ions have comparable conductances, the membrane potential will split the difference btwn equilibrium potentials of these ions
True or false: Since most cells are more permeable to K+ than Na+, the resting membrane potential is closer to that of the equilibrium potential of Na.
False. It is closer to the equilibrium potential of K (EK)
Discuss how Cl- affects resting Vm.
Since Cl- is not actively transported, it has no effects on resting Vm. Therfore, the resting membrane potential determines the concentration gradient for Cl-. (Resting potential is determined by the permeability ions like Na+ and K+ that are actively transported). Cl- just assumes a transmembrane concentration difference that is appropriate for the transmembrane potential. However, Cl- is still important to resting membrane potential. Changes in membrane potential (AP, synaptic potentials) are of relatively short duration while time required to change transmembrane Cl- concentration is much longer. If Vm transiently changes, the membranes 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 membrane potential-important in inhibitory synaptic inputs
Discuss the contribution of the Na+/K+ pump to Vm.
The Na+/K+ pump is electrogenic in nature due to it exchanging an uneven number of ions (3 Na+ out, 2 K+ in making membrane more permeable to K+). Thus, there is a net movement of charge. It contrbutes about 10 mV or less to resting membrane potential so is ignorged in the GHK equation. Its contribution can be greater in some cells. This pump is also important in cell volume regulation.