1. Why study real brains?

   * The 100 step argument.
        Neurons are slow (500 Hz peak firing rate)
        Recognition is fast (a few hundred msec)
        At that rate, at most 100 processing steps can be involved.

        Nature has smarter algorithms than we do.  
        Knows how to exploit parallelism.

    * Hardware design.
        Signal processing in retina and cochlea: analog circuit design.
        Sensor design; molecular computing; etc.

    * Prosthtics.
        John Wyatt's retinal implant.
        "Neuromancer" type brain implants.


2. Organization of real neurons.
       axon, dendrite, soma, synapse
       epsp, ipsp
       ion channels responsible for current flows
       action potentials initiated at axon hillock
       refractory period

       Some numbers:
         10^12 neurons in the human nervous system (a trillion)
         10^15 synapses (quadrillion)

         rats: 10^10 neurons, 10^13 synapses

	 dozens of cell types

         a single cortical neuron may have 10,000 synapses
         Purkinje cells have 200,000

         In a square mm of cortex, each cortical neurons contacts
         roughly 3% of its neighbors; most connections are between
         cells of different types

3. Connectionist units vs. real neurons (show table)

   Firing properites of real neurons:
       spatial summation of inputs (like ANNs)
       temporal summation of inputs
       accomodation: small sub-threshold stimulus can make neuron fail to 
         respond to a just-subsequent supra-threshold stimulus
         (due to channels opening and then inactivating)
       postinhibitory rebound: removing an inhibition can cause a spike
         (inhibition reduces channel inactivation)

4. Blind imitation is useless

    * Making units more "neuron-like" is not productive unless we
      know how to explit these neuron-like properties.

      --> Real neurons are slow (1 msec).  Would our ANN models be
          magically better if we made them as slow as real neurons?

     * Slavish imitation: replace real-valued output with a frequency
       coding (spike rate).  What's the point?

     * Why have spikes?
          physiological advantages -- efficient transmission?
          richer encoding? (phase, frequency, pulse characteristics)

5. How real neurons work

     * Cell membrane blocks ion flow
     * Inside: high concentration of organic anions (A-) and potassium (K+)
       Outside: high concentration of sodium (Na+) and Chloride (Cl-)
           In squid giant axon:
                 Cytoplasm (mM)       Extra-cellular (mM)
          K+          400                    20
          A-          385                     0
          Na+          50                   440
          Cl-          52                   560

     * Ion-selective channels, predominantly K+ channels, allow passive
       flow of ions across the membrane.

     * K+ concentration gradient is outward, so K+ flows out of the cell
       Cell becomes negatively charged relative to outside, so the
         electrotonic gradient is inward
       Negative charge attracts positive ions, but only K+ can enter
       Result:  not all the K+ leaves the cell; only enough leaves to
         bring the voltage to the Nernst potential of -75 mV

       Negative internal charges cluster near the cell membrane; positive
        external charges cluster near the membrane too

       Cell membrane is only 50 Angstroms (10^-10 m) thick, so -70 mV potential
       is like 140,000 volts across a 1 cm membrane: very strong field

       Actual resting potential is closer to -55 mV.  Why?
       There are some passive sodium channels, so a limited inward Na+ current.
       There is a K+/Na+ pump that pumps out 3 Na+ ions for every 2 K+ ions
         it takes in.

     * Voltage gated channels lead to action potentials.

       Voltage gated Na+ channel opens at +10 mV.
       Na+ rushes into the cell, making it even more positive: voltage spike.
       Na+ channels have very high conductance: 10^7 ions/second.

       Neighboring segments of membrane become depolarized; the result
       is an action potential that travels down the membrane.
       Charges are within 10 Angstrom of the membrane wall; they
        don't move very far.  The whole cell interior doesn't participate
        in an action potential; everything happens close to the membrane.

       Na+ channel inactivation: channels spontaneously close again.

       Voltage gated K+ channel is slower to open; stays open as long as
        the cell is depolarized.
       K+ rushes out of the cell, driving it back down to negative again.
       This causes the voltage-gated K+ channels to close again.
       Cell can hyperpolarize if enough K+ ions flow out, dropping to Ek.

       Calcium channels: at least 40 different types
       Very little calcium inside the cell, so calcium current is small.
       Calcium-gated potassium cannels K(Ca) can have inhibitory effect:
         small positive Ca2+ current flows in, causing large K+ current out
       Calcium also needed at the synapse to cause vesicle release
       Calcium also involved in many cell metabolic processes:  seizures
         can cause cell damage because firing causes excessive calcium uptake
         which screws up the cell's metabolism

       The R15 cell in Aplysia (parabolic cell)
          spike rate increaes and then decreases
          then a long refractory period.  total period 10 sec.
          this behavior is the product of 7 different channel types

    * Transmitter-gated channels in the dendrites

    * Transmitters are small molecules: ACh, serotonin, glutamate, GABA
      Same chemical might be excitatory in some cases, inhibitory in others
      Cells also release neuropeptides; regulatory function?

6. How learning happens: in search of the Hebb synapse

   How can weights change?
   Presynaptic:
     Change in amount of transmitter released per vesicle
     Change in rate of vesicle release
   Postsynaptic:
     Change in number of receptors
     Change in spine geometry (receptors become uncovered)
     Change in receptor properties/effectiveness

   Hebb's idea: synaptic strength = strength of correlation between
   firing of pre- and post-synaptic neurons

   The NMDA (N-methyl-D-aspartate) receptor:
   Requires both glutamate binding (evidence of presynaptic activity), and
   cell must be depolarized by 30 mV (postsynaptic response).
   Other properties:  blocked by Mg2+; also has binding sites for
     Zn2+, glycine, PCP, MK801 (experimental drug) which regulate
     channel function.
   Channel passes Ca2+, Na+, and K+.  Principal effect is thought to
   be inward Ca2+ flow triggering second messengers.

