C2006/F2402 2005 Outline of Lecture #17 – Electrical Communication #1

C2006/F2402 -- 2010 --Outline of Lecture #15 – Electrical Communication #1

(c) Stuart Firestein, Columbia University, New York, NY. Last update 3/19/2010

Original Notes by Chris Kelly, 2005

1. Neurons: structure and function

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  The brain –– why is it so special?
  
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    We connect it with our idea of “self” and believe personality resides there.
    
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    Tremendous diversity of cell types and structures.
    
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    Retains plasticity (an ability to modify itself) throughout life
    
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      As the brain undergoes experiences and environmental conditions, it changes itself to adapt.
      
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      Despite this, the brain is the most developed of organs, meaning that its cells are among the most differentiated. Remember that neurons do not divide –– they are permanently in G₀ phase.
      
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  The main function: information transfer and signaling
  
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    The basic circuit: the body encounters a stimulus, peripheral nerves produce an afferent (incoming) signal that comes into the brain (or spinal cord) for processing. The result is an efferent (outgoing) signal, carried through nerves, to some target, resulting in a behavioral response.
    
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      You step on a thumbtack, a pain signal goes to the spinal cord, contacts a motorneuron, signal goes out to the leg muscle, leg retracts.
      
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  Two major divisions: central nervous system (CNS) and peripheral nervous system (PNS).
  
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    CNS: brain and spinal cord.
    
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    PNS: everything else (motoneurons, sensory neurons).
    
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      There are a few exceptions: the retina, for example, is in the back of the eye but is considered part of the CNS.
      
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  The functional unit is a neuron.
  
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    There are 10¹¹ neurons in the adult human brain.
    
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    Neurons were not always recognized as distinct cells: until Ramon y Cajal proved otherwise, people believed there was one big interconnected “nerve net.”
    
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    Neurons can be extremely large (up to 40 meters long in a whale) or extremely small.
    
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    There are two main consequences of Ramon y Cajal’s discovery that neurons are distinct units:
    
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      1) The law of dynamic polarization: information only moves in one direction down a neuron (most of the time).
      
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      2) Specific connectivity: the specificity of the connections in the nervous system is critical. Think of the wires behind your stereo.
      
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  Glial cells are support cells in the brain.
  
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    Glial cells are not involved in signaling; rather, they provide structure, dole out trophic factors, regulate metabolism, contribute to immune response, construct the blood-brain barrier, etc.
    
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    FYI: There are several kinds of glial cells: astrocytes, Schwann cells,  oligodendrocytes are a few.
    
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    There are 10¹² glia in the brain –– a full order of magnitude more than neurons.
    

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  Major parts of the neuron, common to nearly all neuron types
  
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    Soma / cell body: site of protein synthesis, metabolism, etc.
    
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    Dendrites (Gr: tree): protoplasmic extensions continuous with the cytosol. These branch and divide, thereby sending projections all over a tissue, and thin as they extend.
    
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    Axon: A long cable that extends from the soma but is functionally distinct from it. If you look at the plasma membrane of an axon, you see that it contains lipids (& proteins) different from those in the soma’s membrane. The axon may branch out, but it remains isodiametric in all of its projections. If a neuron is particularly large, as in the whale, it is because its axon is long.
    
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    Synaptic terminal: sometimes referred to as the “bouton.” It is the end of the axon that contacts a dendrite, muscle, etc.
    
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  We can now revisit the dynamic polarization principal of Cajal.
  
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    Information enters the dendrites, travels through the tree to the soma, then (if it meets the threshold) enters the axon, and travels its length until the synaptic terminal, which then passes the signal to the next cell.
    

II – Membrane Potential

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  We keep referring to a “signal” –– what is it?
  
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    A signal is encoded as changes in membrane potential.
    
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  Membrane potentials
  
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    Refers to voltage created when the cell separates charges on opposite sides of the membrane. It puts work into separating opposite charges, thereby creating potential energy as voltage.
    
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    Voltage always refers to two points: i.e. here with respect to there. “There” is usually ground; in physiology, ground is the outside of the cell. So, voltage refers to the inside of the cell with respect to the (neutral) outside.
    
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      If the cell’s potential is –50 mV, then the cell is negative with respect to the surround interstitium.
      
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  How can you measure potential?
  
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    Use an electrode.
    
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      An electrode is an extremely thin glass capillary with an open tip that is about one micron in diameter. You fill the electrode with a conducting salt solution and insert a wire connected to a voltmeter. You then poke the electrode through the cell membrane and measure the intracellular potential against that at ground.
      
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      This method reveals that neurons usually have negative resting membrane potentials, between –50 and –90 mV. This potential is often referred to as V_m.
      
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  What constitutes and creates this resting membrane potential?
  
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    In electronics, potentials and current come the position and movement of electrons. In cells, we are not concerned with electrons, but with ions.
    
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    Common ions involved in establishing V_m:
    
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      Sodium (Na⁺)
      
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      Potassium (K⁺)
      
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      Calcium (Ca⁺⁺)
      
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      Chloride (Cl^-)
      

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  How does the potential arise?
  
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    The cell maintains an asymmetric distribution of ions across the membrane and makes the membrane selectively permeable. Both of these merit further discussion.
    
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    Asymmetric distribution:
    
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      Plasma membrane is lipids, so charged particles cannot pass through unless it’s through a pump (like the Na/K ATPase) or channel.
      
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      A typical distribution is:
      

	Inside	Outside
[Na^+]	10 mM	130 mM
[K^+]	140 mM	5 mM

 

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  Other ions involved
  
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    Inside: negatively-charged proteins, chloride
    
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    Outside: chloride, calcium
    
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  Just having this distribution is not enough, however: we still haven’t created any potential. Potential only arises when SOME of the ions can get through the membrane. This is achieved through having selectively permeable channels in the membrane.
  
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    Let’s say we poked some holes in the membrane that only permeated potassium … NOT sodium.
    
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      The first response will be for potassium to flow down its concentration gradient, out of the cell.
      
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      This outward flow leaves behind unpaired anions within the cell, though. Eventually, the negative charge inside the cell will become so great that the diffusive force on the potassium ions, directed outward, will be outweighed by the electrical force on the potassium ions, directed inward to the negatively charged cytosol. An equilibrium condition is then created where the number of ions leaving the cell equals the number of ions entering the cell.
      
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      We can then say that potassium has reached an equilibrium condition, which has an associated electronic potential, measured as E_K= -91 mV.
      
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        We can make a similar calculation for sodium, if we make the cell selectively permeable to sodium ONLY: E_Na= +50 mV.
        
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        Think about where the diffusive force will drive sodium, and where the electrical force will drive it. Refer to the concentrations above.
        
        
        
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  This is the Qualitative description of how this happens. We can gain a deeper appreciation if we also derive a Quantitative description. This description was first developed to understand electrochemical forces in batteries by the Biophysicist Walter Nernst in 1888. It works, remarkably, for your brain as well, because your brain is an electrochemical device.
  

So here’s the derivation:

1. KA dissociates into K+ and A- ions
2. K+ are able to move down their concentration gradient and flux from side 1 to side 2. This is simple movement by diffusion and the work that is done to concentrate ions on one side or the other can be described by the relation:
W_c = RT ln (c2/c1)
R = gas constant (related to energy of the ionic solution)

T= absolute temperature (higher temp=more movement)

ln c2/c1 because this is same as (ln c2 - ln c1). (We use ln – natural log -- because diffusion is an exponential process)
3. But as K+ ions diffuse down their concentration gradient they are leaving behind an excess of negative charges on side 1 and at the same time an excess of positive charges is building up on side 2. This creates a potential (electrical) difference between the two sides.
4. What effect will this have on the K+ ions trying to move down their concentration gradient???

It will oppose this movement by performing electrical work in the opposite direction. K+ ions will find it harder to get to the more positive side because like charges repel. Also A- charges will be holding them back.

This electrical work can be described by:
W_e= zFE

z=valence

F=faraday (analogous term to R for electrical particles)

E=potential difference (like concentration difference)

5. At some point the chemical work in direction 1 to 2 will be exactly opposed by the electrical work in direction 2 to 1. So:
W_c=W_e
zFE = RT ln (c2/c1)
rearranging: E_k= RT/zF ln (c2/c1)

This is the NERNST EQUATION. (1888 Walter Nernst)

More on the Nernst Equation:

Keep in mind that there are still 2 processes at work here.

Note that this describes an EQUILIBRIUM CONDITION.

No energy input is required.

If the membrane is selectively permeable to K+, this situation will occur naturally.

Let's simplify the equation a little more:
for K+ ion at room temp, RT/zF= 25 mV

change from ln to log by (X2.303)

E= 58 log (c2/c1)
CONVENTIONS

measure voltage as side 1 wrt side 2.

in cells measure as inside wrt outside
Lets look at a "real" cell using the K+ ion concentrations given in the table.
E_K= -91 mV.

Let's try this for Na+ also, just for fun.

E_Na = +65 mV

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  If we measure the resting membrane potential of a neuron, we see it is around –75 mV. This is between the equilibrium potentials for potassium and sodium, but closer to that of potassium. So, we see that the cell is mostly permeable to potassium, but also slightly permeable to sodium.
  
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    What would the RMP (resting membrane potential) be if the situation were reversed, if the cell were more permeable to sodium than to potassium?
    
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  The RMP of a cell, then, is found by individually weighting the equilbrium potentials of the various ions involved, based on the membrane’s permeability to each one. Then you just add. This is quantified by the GHK (constant field) equation; see book for details if you’re interested.
  
  
  

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  So far, we have referred to selective permeability without discussing how it arises. The cell creates it with ion channels.
  
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    Ion channels are sophisticated transmembrane proteins that form a selective aqueous pore in the membrane. The channels have some important properties:
    
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      1) They are highly selective.
      
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        Channels become selective by varying their shape/size and flanking certain regions of the pore with positive or negative charges. The degree of selectivity can vary: some only let cations through; others only let potassium through. See book for details.
        
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      2) They have a specific degree of conductance.
      
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        Some are fairly big and allow lots of ions through; others are smaller.
        
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      3) They are gated.
      
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        In order to control the membrane potential, the neuron must be able to control the open/closed status of its various channels. For now, we will only consider voltage-gated channels (i.e. channels that only open when faced with a certain voltage range); in synaptic signaling, we will see the importance of ligand-gated channels.
        
        
        
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  How do you detect these ion channels? They are too small to be seen. Instead, scientists use a method known as patch clamping.
  
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    One applies a glass electrode, as described above, to the membrane of a cell. Applying a little bit of suction causes a piece of the membrane to become attached to the electrode; one can then pull off the electrode and take the membrane section with it. Because the seal between the electrode and the membrane piece is very tight, one can then treat the inside of the electrode and the bath in which you place it as different sides of the cell.
    
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    Once you have isolated one or two channels in your membrane fraction, you can measure the current that flows through them, given certain conditions. This current is on the order of picoamps. (For reference, electronics typically use 10-20 A –– thirteen orders of magnitude greater.)
    
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      The trace you see after measuring the current reveals that individual channels open and close very quickly and apparently randomly. By varying the voltage to which the channels are subjected, however, one can vary the length of time those channels will remain open (or closed).
      
      
      
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  To keep everything straight:
  
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    Equilibrium potential: applies to specific ions
    
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    Resting membrane potential: describes the overall potential of the membrane, based on the contributions of each ion’s weighted equilibrium potential
    
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    Action potential: rapid and invariant change in membrane potential, to be described next.
    

III – Action Potentials

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  So far we have talked about static situations –– resting membrane potentials. How do you change this potential to create an electrical signal?
  
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    The cell uses action potentials, which are rapid, transient, and invariant changes in V_m. The whole process takes 2-3 ms.
    
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    What does invariant refer to?
    
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      The shape, size, and duration of an action potential is always the same, for reasons to be explained next time. The only variable aspect is the frequency at which they occur.
      
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    If action potentials are always the same, how can you encode anything?
    
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      Frequency: different frequencies indicate different stimulus intensities, quantities. A typical firing frequency is between 4-40 Hz, though neurons can fire at 100 Hz or faster.
      
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      Pathway: connections are specific, so an action potential down a certain neuronal tract is assumed to code for a certain stimulus quality. That is, an electrical signal in the optic nerve must, by definition, code for a visual stimulus. (Or, by occurring in the optic nerve, an action potential is assumed to be coding for visual stimulus.)
      
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      Population frequency: Sometimes, stimulus intensity is also coded for by the number of relevant neurons firing action potentials at the same time.
      
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  General terms to describe changes in membrane potential:
  
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    Hyperpolarization; change in voltage in the negative direction. A cell that goes from –40 mV to –70 mV has hyperpolarized.
    
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    Depolarization: change in voltage in the positive direction. A cell that goes from –40 mV to –20 mV has depolarized. So has a cell that goes from +20 to +40 mV.
    
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  Action potential was discovered by recording from the squid giant axon.
  
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    Several distinct phases:
    
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      1) Slight, steady depolarization
      
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      (threshold crossed)
      
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      2) Rapid depolarization – the “spike” in the picture. This is called the rising phase.
      
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      3) Rapid hyperpolarization, the downward part of the spike. This is called the falling phase.
      
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      4) Undershoot: the cell hyperpolarizes beyond its resting membrane potential. While it is extra hyperpolarized, it is in the refractory period and cannot fire another action potential until it starts to move back toward normal RMP.
      
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  How do these various phases arise?
  
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    As expected, through changes in relative permeabilities.
    
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      During depolarization, sodium channels open. The sodium equilibrium potential of +50 is thus weighted more heavily, and the cell’s voltage moves toward it.
      
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      The cell enters the rising phase because lots of sodium channels suddenly open. So the +50 value is weighted even more heavily.
      
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      All of a sudden, lots of potassium channels then open. The potassium equilibrium potential is now the more heavily weighted, so the cell races back down toward –75 mV … this is the falling phase and undershoot.
      
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      The cell then equilibrates the Na and K permeabilities to normal and reaches standard RMP.
      
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        IMPORTANT: at no point have you changed the concentrations on either side of the membrane! Ions are indeed moving, but these changes are negligible as far as concentrations are concerned. All that has thus really changed are the RELATIVE permeabilities to the various ions, and thus which ones contribute more strongly to the cell’s membrane potential.
        
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        Firing an action potential, then, simply involves changing the number of open channels permeating a particular ion.
        

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  Recall that there are no appreciable changes in concentration at any point in this action potential. All that has changed are the relative permeabilties of potassium and sodium.
  
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    In fact, were you to poison the Na/K pump, eliminating the cell’s ability to restore those ions to the correct side of the membrane, the neuron could still fire another 150,000 action potentials before the concentrations started to become insufficient.
    
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  Notice that there is little room for variety in this process, which is why action potentials are (1) invariant, and (2) all-or-nothing. You cannot have half of an action potential.
  

To review the action potential, try problem 8-2, A-C, & 8-3 to 8-4.