2017-09-20 19:25:52

Ease on down, ease on down

Propagation is the way…

Today's Topics

  • Equilibrium potential and driving forces
  • The action potential
  • Synaptic communication

Party On

  • Annie (A-) was having a party.
    • Used to date Nate (\(Na^+\)), but now sees Karl (\(K^+\))
  • Hired bouncers called
    • "The Channels"
    • Let Karl and friends in or out, keep Nate out
  • Annie's friends (A-) and Karl's (\(K^+\)) mostly inside
  • Nate and friends (\(Na^+\)) mostly outside
  • Claudia (Cl-) tagging along

Party On

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 remains near membrane
  • Separation from \(A^-\) creates charge \(\frac{K+K+K+K+K+}{A-A-A-A-A-}\) along capacitor-like membrane
  • \(V_m\) –> \(V_{K}\)

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 \(V_{K}\) (-90 mV) than \(V_{Na}\) (+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" and equilibrium potential

  • "Driving Force" on a given ion depends on difference between
    • Equilibrium potential for given ion
    • Membrane potential = effects of all ions
  • Anthropomorphic metaphor
    • \(K^+\) "wants" to flow out (pull neuron toward \(V_{K}\))
    • \(Na^+\) "wants" to flow in (pull neuron toward \(V_{Na}\))
    • Strength of that "desire" depends on distance from equilibrium potential

Action potential

Action potential

  • Rapid rise, fall of membrane potential
  • Threshold of excitation
  • Increase (rising phase/depolarization)
  • Peak
    • at positive voltage
  • Decline (falling phase/repolarization)
  • Return to resting potential (refractory period)

Action potential components

Phase Neuron State
Rise to threshold + input makes membrane potential more +
Rising phase Voltage-gated \(Na^+\) channels open, \(Na^+\) enters
Peak Voltage-gated \(Na^+\) channels close and deactivate; voltage-gated \(K^+\) channels open
Falling phase \(K^+\) exits
Refractory period \(Na^+\)/\(K^+\) pump restores [\(Na^+\)], [\(K^+\)]; voltage-gated \(K^+\) channels close

Action potentials and driving forces

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 \(Na^+\) high (-90 mv - 55 mV = -145 mV), but too bad

Absolute refractory phase

  • Voltage-gated \(K^+\) channels closing
    • Driving force on \(K^+\) tiny or absent
  • \(Na^+\)/\(K^+\) 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

Review AP phases and driving forces

Neuron at rest

  • Voltage-gated \(Na^+\) closed, but ready to open
  • Voltage-gated \(K^+\) channels closed, but ready to open
  • Membrane potential at rest
  • \(Na^+\)/\(K^+\) 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 in 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

APs and Information Processing

Information processing

  • AP amplitudes don't vary (much)
    • All or none
    • \(V_{K}\) and \(V_{Na}\) don't vary much b/c \(Na^+\)/\(K^+\) pump always working
  • AP frequency and timing vary
    • Rate vs. timing codes
    • Same rates, but different timing
    • "Grandmother" cells and single spikes

Information processing

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, 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

Hodgkin-Huxley Equations

More on HH

Synaptic transmission

What happens when AP runs out of axon?

  • Rapid change in voltage triggers neurotransmitter (NT) release
  • Voltage-gated calcium Ca++ channels open
  • Ca++ causes synaptic vesicles to bind with presynaptic membrane, merge
  • NTs diffuse across synaptic cleft
  • NTs bind with receptors on postsynaptic membrane
  • NTs unbind, are inactivated

Receptor/channel types

  • Leak/passive
    • Vary in selectivity, permeability
  • Transporters/exchangers
    • Ionic
      • \(Na^+\)/\(K^+\)
    • Chemical
      • e.g., Dopamine transporter (DAT)

Receptor/channel types

  • Ionotropic receptors (receptor + ion channel)
    • Ligand-gated
    • Open/close channel
  • Metabotropic receptors (receptor only)
    • Triggers 2nd messengers
    • G-proteins
    • Open/close adjacent channels, change metabolism

Gap junctions

  • Cytosol flows through adjacent neurons

Chemical synapse

Receptor types

Receptors generate postsynaptic potentials (PSPs)

  • Small voltage changes
  • Amplitude scales with # of receptors activated
  • Excitatory PSPs (EPSPs)
    • Depolarize neuron (make more +)
  • Inhibitory (IPSPs)
    • Hyperpolarize neuron (make more -)

NTs inactivated

  • Buffering
    • e.g., glutamate into astrocytes
  • Reuptake via transporters
    • e.g., serotonin via serotonin transporter (SERT)
  • Enzymatic degradation
    • e.g., AChE degrades ACh

Questions to ponder

  • Why must NTs be inactivated?
  • What sort of PSP would the following induce:
    • Open \(Na^+\) channel
    • Open \(K^+\) channel
    • Open Cl- channel, \([Cl^-]_{out}\)>>\([Cl^-]_{in}\)

Types of synapses

References

Eyherabide, Hugo G., Ariel Rokem, Andreas V. M. Herz, Inés Samengo, Hugo G. Eyherabide, Ariel Rokem, Andreas V. M. Herz, and Inés Samengo. 2009. “Bursts Generate a Non-Reducible Spike-Pattern Code.” Frontiers in Neuroscience 3: 1. doi:10.3389/neuro.01.002.2009.