Membrane Biophysics and Electrochemical Signaling

Dr. DeBello, Fall 2024, Lectures 4-8

How are motor outputs produced?

• The brain receives sensory signals, processes them, and produces a motor output

Perception

• What you can report on

How many neurons/ synapses does the human brain have?

• 86 billion neurons and interconnected by 100+ trillion synapses

• The brain relies on neurons specialized for chemical and electrical signaling

• The brain is a synaptic network

How do neurons communicate with each other?

• Neurons communicate with other neurons using neurotransmitters (chemical messengers) which are released and detected by synapses

Electrical Signaling

• Ion movement across the plasma membrane is the basis of electrical signaling in neurons

Ion/ molecule movement

• Two types of transmembrane proteins, carriers and channels

Carrier-Mediate Transport (ion movement)

• Transporter protein, has a solute-binding site and flips orientation when bound, allowing the solute to diffuse into the cell

• Ligand specific

• Facilitated diffusion uses a fixed affinity site and transports down the concentration gradient

• Pumps have variable affinity sites and transport uphill, against the concentration gradient

Facilitated Diffusion (carrier-mediated transport)

• Uses a fixed-affinity site and transports down the concentration gradient

• Increase in concentration means the molecules are more likely to bind

• The energy of binding triggers a conformational rearrangement that exposes the binding site to the opposite side of the membrane

• Passive Transport

Membrane Pump (carrier-mediated transport)

• Variable affinity sites and transports against the concentration gradient

• Active transport

Sodium/ Potassium ATPase

• Pump that transports 3 Na+ in to and 2 K+ out of the cell with each cycle

• Establish and maintain the concentration gradients for Na+ and K+ ions

Ion Channel (ion movement)

• Channel protein, pore that allows for diffusion-like permeation

• No binding site

• Differ in selectivity, permeability, and gating

Driving Forces

• Two kinds, electrical and chemical

• Net force that drives an ion to move across a cell membrane

• At any moment, each driving force can be represented by a vector which has direction and magnitude

• At any moment, ions experience a net driving force which is the vector sum

Chemical Driving Force

• Diffusion down a concentration gradient

Electrical Driving Force

• Results from electrostatic attraction or repulsion at a distance

Membrane Potential

• Voltage difference across the plasma membrane

• By convention the polarity is referenced inside relative to outside

• Neurons

Charge Seperation

• The amount of charge separation underlying biologically meaningful electrical signaling is extremely small compared to the total number of ions in bulk solution on both sides of the membrane

• Therefore Na+ and K+ concentration gradients don’t run down during normal physiological operation

Equilibrium Potential E_ion

• Membrane potential at which there is no net charge movement for that ion

• Calculated with the Nernst equation

E_K+

• -90mV outward

• Higher concentration of K+ inside the cell

• Wants to leave cell

E_Na+

• +60mV inward

• Higher concentration Na+ outside the cell

• Wants to enter cell

Nernst Equation for E_ion

• At equilibrium potential of an ion…

  • electrical driving force = chemical driving force

  • equilibrium potential = magnitude of concentration gradient

  • equilibrium potential = membrane potential (voltage drop)

Resting Membrane Potential

• Voltage difference across the plasma membrane when the cell is at rest

• Depends on all the permeant ion species wighted bytheir relative permeabilities

• At rest, K+ dominates as there are more K+ leak channels than Na+ leak channels

• Calculated using the GHK equation

• -70mV

Graded Potential

• Transient injection of current leads to passive dissipation of current regardless of the current source, this causes a graded potential

• Local changes in membrane potential that decay over short distances

• Always decreases in size as it flows away form the current source

• Self-limited in time and space

Action Potential/ AP/ Spike

• Electrical signals initiated by the axon hillock which rapidly propagate to the axon terminals where they trigger transmitter release

• All-or-nothing event

• Net driving force on Na+ is stronger at action potential onset and weaker at action potential peak

• Net driving force on K+ is weaker at action potential onset and stronger at action potential peak

What do action potentials depend on?

• Voltage-gated Na+ and K+ ion channels

• These channels produce voltage-dependent, time variant changes in membrane permeability to Na+ and K+

Threshold Potential

• The membrane potential that once crossed causes depolarization of the axon via a positive feedback loop

• depolarization → Na+ channels open → influx of Na+ → more depolarized, etc

• about -50mV

Linear sequence of action potential

1. At rest, ion channels are deactivated, membrane potential is at -70mV

2. Triggering event causes Na+ activation gate to open, strong inward driving force of Na+, membrane potential reaches threshold potential

3. Na+ gate fully opens, continues to drive membrane potential to E_Na+ of +60mV

4. Hits peak membrane potential around +30mV, ball and chain swing and inactivate Na+ channel, K+ gate opens

   1. The Na+ activation gate is still open, can not be reactivated at this state

5. Membrane potential is decreasing as K+ leaves the cell with a large driving force

6. The cell hyperpolarizes, causes Na+ gate to deactivate

7. Both channels are deactivated and membrane potential returns to -70mV, cell can be activated again

Absolute Refractory Period

• Brief period (~1ms) during which the neuron cannot fire another action potential regardless of the strength of new triggering event

• Begins when all Na+ channels have opened (when threshold reached) and ends when the Na+ channel inactivation is removed

Relative Refractory Period

• Brief period (few ms) during which the neuron can fire another action potential but would require a larger than usual triggering event

• Begins when Na+ inactivation is removed and ends when resting potential is restored following K+ channel deactivation

What does speed and reliability of action potential depend on?

• Axonal diameter

• Membrane resistance

• Internal resistance

• Presence or absence of myelin

Contiguous Conduction

• Relies on continuous distribution of voltage gated Na+ and K+ channels along the length of the axonal membrane

• Active process

• Not self-limited in time and space

• Stadium wave

Saltatory Conduction

• Relies on myelin (insulation) and clusters of voltage gated Na+ and K+ channels found at the Nodes of Ranvier

• Active process at the sites of initiation and nodes of ranvier

• Passive process (graded potential) underneath the myelinated stretches of the axon

Myelin

• Increases relative permeability of propagation and speed

• Multilayered sheath of plasma membrane that wraps around axons and acts as an insulator to the flow of current

• Current flows down the length of the axon not out through the membrane

• Decreases capacitance (amount of charge that can be stored) and therefore lowers the time constant which results in the membrane potential changing faster in response to current injection

Nodes of Ranvier

Gaps in the myelin containing a high density of voltage gated Na+ and K+ channels

How far current will flow down the axon before leaking out depends on what?

• The relative values of membrane resistance (transverse path) and internal resistance (axial path)

• In giant axons, internal resistance is low which favors action potential propagation

• In narrow axons like those in our brain, internal resistance is high which favors leak out and poor propagation

• Myelin increases membrane resistance such that the axial path is now the lower resistance path

What does Na+ channel inactivation ensure?

• Unidirectional spread of naturally occurring action potentials

• The annihilation of action potentials experimentally induced at either end of the axon when they collide

Demyelinating Disease

• Result in slow and unreliable action potential propagation

• Multiple sclerosis (autoimmune disease) commonly affects the cerebellum, a brain structure which plays an important role in calibrating ongoing movement, the symptoms are ‘action tremors’ (covered more in lecture 13)