Cell and Organ Systems Biology

 

Ion Channels and Membrane Transport - 2000

 

Jim Huettner

6600 Cancer Research Building

mailto:huettner@cellbio.wustl.edu

362-6624

 

The handout you received contained:

 

1)  Notes for the following three lectures:

 

2)  Study questions covering the material in these lectures.

 

3)  Several homework questions and answers from previous years that supplement material in the lecture notes.

 

4)  All of the overheads for the lectures.

 

In addition, you may wish to read:

 

Costanzo, Physiology                      chapter 1 (pg. 1-24)

 

Lodish et al., 3rd ed.                         chapter 15 (pg. 633-656; 661-664)

Molecular Cell Biology                    chapter 21 (pg. 932-971)

Alberts et al., 3rd ed.                        chapter 11 (pg. 507-547)

Molecular Biology of the Cell         also read pages 667-670

 

Objectives:

 

This section is focused on two main topics: 1) The electrical properties of cells. 2) The role that energy balance plays in cellular processes, with emphasis on membrane transport. These two topics are fundamental to all of the subsequent sections of the course. Electrical signaling underlies the operation of the brain, the heart and skeletal muscle. Membrane transport is required in all cells, but is particularly important for secretion in organs such as the kidney, lung, stomach and pancreas.

 

The major goal of these sessions is to help you understand the basic chemical and physical principles that underlie electrical properties of cells and the movement of ions and other solutes across the cell membrane. By the end of the section you should understand the ionic basis of the resting and action potential. In addition, you should understand how energy balance will influence a cell's ability to move solutes across its membrane.

 

 

Learning Objectives:

 

·        After completion of this section you should understand why all cells need to express ion channels and you should understand the electrical consequences for the cell of expressing ion channels in its surface membrane.

 

·        You should understand why individual ions are not uniformly distributed across the cell membrane and you should understand how this unequal distribution is established and maintained.

 

·        You should understand why this unequal distribution of ions gives rise to a resting membrane potential. You should understand how the membrane's permeability to ions and the distribution of ions control the membrane potential.

·        You should understand why different mechanisms of membrane transport are required for different types of chemical compounds that the cell wishes to move across its plasma membrane. You should understand the physical properties that determine whether or not a particular compound will freely permeate through the membrane.

·        You should understand why solutes that must bind to a proteinaceous carrier exhibit different kinetics of membrane transport than do freely permeable solutes.

·        You should understand why the energy available from ATP is not constant, but instead, depends on the concentration of reactants and products. You should understand how the energy of a solute concentration gradient is calculated.

·        You should be able to compare the energy available from ATP with the energy required to transport solutes across the membrane. You should understand how the energy stored in an ion gradient can be used to drive the transport of another solute.

·        You should understand the energetics and regulation of acid secretion in the stomach. You should understand why interconversion of carbon dioxide and bicarbonate, coupled with chloride-bicarbonate exchange, is important for acid secretion and for the transport of products of respiration in the blood.

·        You should understand how the membrane potential is measured experimentally and how the membrane capacitance and resistance determine the time course of changes in membrane potential.


·        You should understand the ionic basis of the action potential. You should understand the channel properties that are essential for generation of an action potential. You should understand the mechanisms that can terminate an action potential.

·        You should understand why there is a threshold for action potential generation and appreciate the factors that set the threshold. You should understand why there is a refractory period following an action potential and why it determines the maximal action potential frequency.

·        You should understand the gating states of voltage-gated sodium channels and the roles that each state plays in determining the action potential time course.

·        You should understand why the final effect of an action potential is to elevate cytoplasmic calcium.

·        You should understand the basic steps in synaptic transmission between a nerve cell and its target. You should understand why, in most cases, transmission is chemical rather than electrical.

·        You should understand the differences between very fast synapses that operate on the time scale of milliseconds and those which change the properties of postsynaptic targets for a period of seconds to minutes.

·        You should understand the differences between an excitatory and an inhibitory synapse.

 

 

Study Questions:   The resting membrane potential

 

1)    Name the different ways that molecules and ions might permeate cell membranes.  What are the essential properties of a molecule that uses each mechanism?

 

2)    Which mechanism(s) will be used by the following molecules.  (a) steroid hormones  (b) glucose  (c) anesthetics  (d) positive ion  (e) negative ion  (f) Vitamin E  (g) water?

 

3)    "Cells are always at water equilibrium!" - What does this mean?

 

4)    Define hypertonic, hypotonic and isotonic.  Which of these three adjectives describes  (a) 100 mM NaCl  (b) 200 mM NaCl  (c) 150 mM NaCl  (d) 300 mM sucrose  (e) 100 mM Na2SO4?

 

5)    What is the difference between the Nernst potential and membrane potential?

 

6)    Under what conditions might the membrane potential equal a Nernst potential?

 

7)    If the membrane potential is positive to the Nernst potential for a positive ion, in what direction will the ion flow through an ion channel in the membrane?  What if the ion is negative?

 

8)    Which ion is closest to equilibrium in a normal cell, K+, Na+, or Ca2+?

 

9)    What features distinguish carrier-mediated diffusion from simple diffusion?

 

10)  What features distinguish passive carrier diffusion from active transport?

 

11)  The Na+ pump helps to keep [Na+]in at 10 to 15 mM.  Why doesn't the pump reduce [Na+]in even lower?

 

Study Questions:   Carriers and pumps in passive and active transport

 

1)    What is a reasonable estimate of the energy in a molecule of ATP?

 

2)    Can a molecule of ATP provide exactly the same amount of energy in every cell?  Explain.

 

3)    Could the energy available to a cell per molecule of ATP change over time?  Why?

 

3)    How much energy is required to pump an uncharged molecule up a 10 fold concentration gradient?

 

4)    How much energy is required to pump a (+) charged ion up a 60 mV electrical gradient?

 

5)    How much energy is required to pump a (+) charged ion up a 60 mV electrical gradient and up a 10 fold concentration gradient?

 

6)    How much energy is required to pump a (+) charged ion up a 60 mV electrical gradient and down a 10 fold concentration gradient?

 

7)    What is the situation described in the last question usually called?

 

8)    If the stomach lumen and the parietal cell cytoplasm are both 70 mV more negative than the circulation, what is the potential difference across the lumenal membrane of the parietal cell? 

 

9)    In the lecture notes, we said [K]cytoplasm @ 145 mM and [K]lumen @ 10 mM, but we did not give values for Cl or Na.  Given your answer to the last question, can you make any predictions about the concentrations of Na and Cl, and about the relative permeability of the lumenal membrane to these ions?

 

Study Questions:   The action potential and synaptic transmission

 

1)    Describe and distinguish current, charge, voltage, resistance, capacitance. What are the units of each? What is a typical cellular amplitude for each?

 

2)    Describe two means by which current passes through cell membranes?

 

3)    "Inward current depolarizes the cell membrane" - explain this statement and the sign conventions behind it.

 

4)    The direction of ion movement across a cell membrane depends on both the membrane voltage and the concentration gradient. How does Ohm's law for a membrane account for these two factors?

 

5)    Why does an instantaneous input of current cause a slow change in membrane voltage?

 

6)    Household wiring conducts electricity at nearly the speed of light (3 X 108 meters/sec), whereas the fastest nerve conducts at 100 meters/sec. Why are nerves so slow compared to metal wires?

 

7)    Describe the gating states of voltage-gated sodium channels during an action potential. What feature of gating determines the refractory period?

 

8)    Why are action potentials said to be "regenerative"?

 

9)    What is the minimum requirement to generate an action potential? That is, how many different kinds of ion channels would be essential and what should their properties be?

 

10)  Action potentials serve as triggers for diverse cellular outputs (secretion, muscle contraction, etc.). What is the common link between the action potential and these subsequent events?

 

11)  What steps are involved in secretion of transmitter at a synapse?

 

12)  What are the advantages of chemical versus electrical transmission?

 

 

 

Homework problems and answers from previous years (3 pages total).

 

1.  In lecture we said that digitalis affects the heart rate by inhibiting the Na+-K+ ATPase, which indirectly elevates [Ca2+]in.  Suppose you have administered enough digitalis to double [Na+]in from 14 mM to 28 mM ([Na+]out = 140 mM).  How much energy is available per Na+ ion and how low could [Ca2+]in be kept under these conditions if sodium / calcium exchange is solely responsible for Ca2+ pumping.  Assume the following:  1) The cell is able to maintain Vm at - 60 mV in spite of the change in [Na+]in.  2) The exchanger uses 3 Na+ per each Ca2+ ion. 

 

 

  DGelectrical         =  - 60 meV

 

  DGchemical         =  60 meV * (log 28   -   log 140)   =   - 41.9 meV

 

       DGTotal       =  - 101.9 meV

 

            3 Na+  Þ  305.7 meV

 

            305.7  =  120  +  60 * log (1.5 / ?)

 

            185.7 / 60  =  log (1.5 / ?)

 

            103.1  =  1.5 / ?

 

            ?  @  1.2 µM

 

 Þ  Doubling of internal Na+ from 14 mM to 28 mM caused nearly a 10 fold rise in the estimated internal Ca2+ concentration.

 

2.  ATP is synthesized by mitochondria using the energy in the proton gradient across the inner mitochondrial membrane.  Protons flow from the cytoplasmic side of the membrane (where pH = 7.0) into the matrix, which is the technical term for the compartment enclosed by the inner membrane (where pH = 7.3).  If 3 protons must pass through the Class F ATPase per each molecule of ATP produced, estimate the voltage difference between the matrix and cytoplasm.  (note - there is no voltage difference across the outer mitochondrial membrane). Assume that each ATP molecule requires 500 meV of energy.

 

H+ moves from outside to inside

 

            DG  =  Gproducts   -   Greactants   =   Ginside   -   Goutside     

 

    DGchemical       =  60 meV * (-7.3 - (-7))     remember   pH = - log [H+]

 

                        =  60 meV * (- 0.3) 

 

                        =  -18.1 meV per proton or - 54.3 meV / 3 H+

 

  DGelectrical  =  DGTotal   -   DGchemical 

 

DGelectrical           =  500 meV (needed per ATP) - 54.3 meV (available from DpH)

 

                        =  445.7 meV (from 3 protons  or  148.6 meV per proton)

 

So       - 148.6 meV   =  (+1e) * (Vin  -  Vout)  Þ  Vin  =  Vout  -  148.6 mV  

The matrix is at least 149 mV more negative than the cytoplasm (actually the voltage gradient has been measured at about 200 mV, matrix more negative than cytoplasm).

 

3.  In Case 3, we assumed that the resting potential of a parietal cell is -70 mV with respect to tissue fluid on the circulation side of the epithelium (cytoplasm is at same potential as stomach contents).  (a) Calculate the energy required per pump cycle if the resting potential is actually -90 mV (cytoplasm is 20 mV more negative than stomach contents).  (b) Repeat the calculation if Vm is -50 mV  (cytoplasm is 20 mV more positive than stomach contents).

 

(a)     H+ moves from inside to outside

 

            DG  =  Gproducts   -   Greactants   =   Goutside   -   Ginside   

 

    DGelectrical       =  (+1e) * (-70 mV)   -   (+1e) * (- 90 mV)   =  + 20 meV

 

    DGchemical       =  + 360 meV

 

    DGTotal          =  DGelectrical   +   DGchemical   =  20 meV   +   360 meV  

 

                        =   + 380 meV  per proton

 

K+ moves from outside to inside

 

            DG  =  Gproducts   -   Greactants   =   Ginside   -   Goutside     

 

  DGelectrical         =  (+1e) * (-90 mV)   -   (+1e) * (-70 mV)   =  - 20 meV

 

  DGchemical         = + 69.7 meV

 

       DGTotal       =  DGelectrical   +   DGchemical  =  -20 meV   +   69.7 meV  

 

                        =   + 49.7 meV  per potassium

 

       DGTotal       =  DGproton   +   DGpotassium 

 

                        =  429.7 meV   required for 1 proton and 1 potassium 

 

(b)     H+ moves from inside to outside

 

    DGelectrical       =  (+1e) * (-70 mV)   -   (+1e) * (- 50 mV)   =  - 20 meV

 

    DGchemical       =  + 360 meV

 

    DGTotal          =  - 20 meV   +   360 meV   =   + 340 meV  per proton

 

K+ moves from outside to inside

 

  DGelectrical         =  (+1e) * (-50 mV)   -   (+1e) * (-70 mV)   =  + 20 meV

 

  DGchemical         = + 69.7 meV

 

       DGTotal       =  20 meV   +   69.7 meV  =   + 89.7 meV  per potassium

 

       DGTotal       =  DGH   +   DGK  =  429.7 meV   required for 1 H and 1 K

 

Þ  Because this is an electroneutral exchange of one + charge for another, increasing or decreasing the potential across the lumenal membrane has an equal and opposite effect on H+ and K+.  The total is the same at Vintracellular = - 90 or - 70 or - 50 mV.