2019-02-06 11:48:50

Today's Topics

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

Another take…

The Hodgkin-Huxley (HH) model

HH model: Membrane as simple circuit

  • 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 \(Vg=I\)

The \(K^+\) story

  • \(Na^+\)/\(K^+\) 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 \(K^+\)

Equilibrium potential

  • 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

Equilibrium potential

  • \(K^+\) 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) –> \(V_{K^+}\)

Equilibrium potentials calculated under typical conditions

Ion [inside] [outside] Voltage
K+ ~150 mM ~4 mM ~ -90 mV
Na+ ~10 mM ~140 mM ~ +55-60 mV
Cl- ~10 mM ~110 mM ~ - 65-80 mV

The \(Na^+\) story

  • \(Na^+\)/\(K^+\) 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)

Resting potential

  • 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)

Resting potential

  • 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" and equilibrium potential

  • "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

"Driving force" and equilibrium potential

  • 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

Action potentials and driving forces

Voltage-gated \(Na^+\) and \(K^+\) channels

  • 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

Neuron at rest

  • 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

Action potential rising phase

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

Peak

  • 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)

Peak

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

Falling phase

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

Absolute refractory phase

  • 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

Relative refractory period

  • 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

Neuron at rest

  • 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…

Phase Ion Driving force Flow direction Flow magnitude
Rest K+ 20 mV out small
Na+ 125 mV in small

Phase Ion Driving force Flow direction Flow magnitude
Rising K+ growing out growing
Na+ shrinking in high

Phase Ion Driving force Flow direction Flow magnitude
Peak K+ 120 mV out high
Na+ 20 mV out small

Phase Ion Driving force Flow direction Flow magnitude
Falling K shrinking out high
Na+ growing in small

Phase Ion Driving force Flow direction Flow magnitude
Refractory K ~0 mV out small
Na+ 145 mV in small

Animation

Generating APs

  • 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

Axon hillock, axon initial segment

AP propagation

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

AP propagation is like

AP propagation

  • 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

Question

  • 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.

Question

  • 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.

Conduction velocities

Information processing

  • 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

Wherefore brains?

Why brains?

Escherichia Coli (E. Coli)

  • 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

Paramecium

  • 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

Caenorhabditis Elegans (C. Elegans)

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

Why brains?

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

Next timeā€¦

  • Exam 1