• Another take on the resting and action potentials
• Action potential propagation
• (if time) Wherefore brains?
• Review for Exam 1

• Membrane as capacitor (C): stores charge
• Ion channels: resistors that can vary in conductance (\(g=\frac{1}{R}\))
• Ion flows create current (I)
• Ohms Law: \(V=\frac{I}{g}\) or \(Vg=I\)

• \(Na^+\)/\(K^+\) pump pulls \(K^+\) in
• \([K^+]_{in}\) (~150 mM) >> \([K^+]_{out}\) (~4 mM)
• Outward flow of \(K^+\) through passive/leak channels
• Outflow stops when membrane potential, \(V_m\) = equilibrium potential for \(K^+\)

• Voltage (\(V_{K}\)) that keeps system in equilibrium
  • \([K^+]_{in}\) >> \([K^+]_{out}\)
• Nernst equation
  • \(V_{K}\) = \(\frac{RT}{(+1)F}ln(\frac{[K^+]_{out}}{[K^+]_{in}})\)
  • \(V_{K}\) = ~ -90 mV
  • Negative in/positive out keeps in/out concentration gradient

• \(K^+\) flows out through passive/leak channels
• Most \(K^+\) remains near membrane
• Separation from \(A^-\) creates charge \(\frac{K+K+K+K+K+}{A-A-A-A-A-}\) along capacitor-like membrane
• \(V_m\) (membrane potential) –> \(V_{K^+}\)

• \(Na^+\)/\(K^+\) pump pushes \(Na^+\) out
• \([Na^+]_{in}\) (~10 mM) << \([Na^+]_{out}\) (~140 mM)
• Equilibrium potential for \(Na^+\), \(V_{Na^+}\) = ~ +55 mV
  • Inside positive/outside negative to maintain outside > inside concentration gradient
• If \(Na^+\) alone, \(V_m\) –> \(V_{Na}\) (~ +55 mV)

• Sum of outward \(K^+\) and inward \(Na^+\)
  • Membrane more permeable to \(K^+\) than \(Na^+\), \(p_{K+}> p_{Na^+}\)
  • Outward flow of \(K^+\) > inward flow of \(Na^+\)
  • Resting potential (~-70 mV) closer to \(Ve_{K}\) (-90 mV) than \(Ve_{Na}\) (+55 mV)

• Goldman-Hodgkin-Katz equation
  • \(V_m = \frac{RT}{F}ln(\frac{p_{K}[K^+]_{out}+p_{Na}[Na^+]_{out}}{p_{K}[K^+]_{in}+p_{Na}[Na^+]_{in}})\)

• "Driving Force" on a given ion depends on difference between
  • Equilibrium potential for given ion AND
  • Neuron's current membrane potential (\(V_m\))
  • \(V_m\) reflects combined effects of all ions

• Anthropomorphic metaphor
  • \(K^+\) "wants" to flow out (hyperpolarize neuron)
  • \(Na^+\) "wants" to flow in (depolarize neuron)
  • Strength of that "desire" depends on distance from equilibrium potential

• Dynamic elements; change state over time
  • HH equations describe state changes
• Open and close with changes in voltage
• Voltage-gated \(Na^+\) also inactivate; de-inactivate as voltage changes

• Driving force on \(K^+\) weakly out
  • -70 mV - (-90 mV) = +20 mV
• Driving force on \(Na^+\) strongly in
  • -70 mV - (+55 mV) = -125 mV
• \(Na^+\)/\(K^+\) pump maintains concentrations

• Voltage-gated \(Na^+\) channels open
• Membrane permeability to \(Na^+\) increases
  • \(Na^+\) inflow through passive + voltage-gated channels
  • continued \(K^+\) outflow through passive channels

• Membrane permeability to \(Na^+\) reverts to resting state
  • Voltage-gated \(Na^+\) channels close & inactivate
  • Slow inflow due to small driving force (+30 mV - 55mV = -25 mv)

• Membrane permeability to \(K^+\) increases
  • Voltage-gated \(K^+\) channels open
  • Fast outflow due to strong driving force (+30 mv - (-90 mv) = +120 mV)

• \(K^+\) outflow
  • Through voltage-gated \(K^+\) and passive \(K^+\) channels
• \(Na^+\) inflow
  • Through passive channels only

• Cannot generate action potential (AP) no matter the size of the stimulus
• Membrane potential more negative (-90 mV) than at rest (-70 mV)
• Voltage-gated \(Na^+\) channels still inactivated
  • Driving force on \(Na^2\) high (-90 mv - 55 mV = -145 mV), but too bad
• Voltage-gated \(K^+\) channels closing
  • Driving force on \(K^+\) tiny or absent
• \(Na^2\)/\(K^2\) pump restoring concentration balance

• Can generate AP with larg(er) stimulus
• Some voltage-gated \(Na^+\) 'de-inactivate', can open if
  • Larger input
  • Membrane potential is more negative than resting potential

• Voltage-gated \(Na^+\) closed, but ready to open
• Voltage-gated \(K^+\) channels closed, but ready to open
• Membrane potential \(V_m\) at rest (~60-75 mV)
• \(Na^+\)/\(K^+\) pump still working…

• Axon hillock
  • Portion of soma adjacent to axon
  • Integrates/sums input to soma
• Axon initial segment
  • Umyelinated portion of axon adjacent to soma
  • Voltage-gated Na+ and K+ channels exposed
  • If sum of input to soma > threshold, voltage-gated Na+ channels open

• Propagation
  • move down axon, away from soma, toward axon terminals.
• Unmyelinated axon
  • Each segment "excites" the next

• Myelinated axon
  • AP "jumps" between Nodes of Ranvier via saltatory conduction
  • Nodes of Ranvier == unmyelinated sections of axon
  • voltage-gated \(Na^+\), \(K_+\) channels exposed
  • Current flows through myelinated segments

• Why does AP flow in one direction, away from soma?
  • Soma does not have (many) voltage-gated \(Na^+\) channels.
  • Soma is not myelinated.
  • Refractory periods mean polarization only in one direction.

• Why does AP flow in one direction, away from soma?
  • Soma does not have (many) voltage-gated \(Na^+\) channels.
  • Soma is not myelinated.
  • Refractory periods mean polarization only in one direction.

• AP amplitudes don't vary (much)
  • All or none
  • \(Na^+\)/\(K^+\) pumps working all the time
  • \([K^+]\) & \([Na^+]\) don't vary much, so
  • \(V_{K^+}\) & \(V_{Na^+}\) don't vary much
• AP frequency and timing vary
  • Rate vs. timing codes
  • Neurons use both

• Escherichia Coli (E. Coli)
• Paramecium
• Caenorhabditis Elegans (C. Elegans)

Sterling & Laughlin, 2015

• Tiny, single-celled bacterium
• Feeds on glucose
• Chemo ("taste") receptors on surface membrane
• Flagellum for movement
• Food concentration regulates duration of "move" phase
• ~4 ms for chemical signal to diffuse from anterior/posterior

• 300K larger than E. Coli
• Propulsion through coordinated beating of cilia
• Diffusion from head to tail ~40 s!
• Use electrical signaling instead
  • Na+ channel opens (e.g., when stretched)
  • Voltage-gated Ca++ channels open, Ca++ enters, triggers cilia
  • Voltage propagates across cell within ms

• ~10x larger than paramecium
• multi-cellular (\(n\)=959)
• \(n=302\) are neurons & \(n=56\) are glia
• Can swim, forage, mate

• Bigger bodies (need to send specific info)
• For neurons (point to point communication)
• Live longer
• Do more, do it faster

• Exam 1