Membrane Electrophysiology

• Summarized notes on membrane electrophysiology

Resting Membrane Potential

• A potential difference exists across the membrane in all living cells, which is measurable using microelectrodes
• In most cells, the membrane potential remains relatively stable and can undergo depolarization or hyperpolarization when stimulated
• Excitable membranes exhibit three basic electrical states: resting, action potential, or graded response
• The resting membrane potential's value depends on: ionic composition of intracellular and extracellular fluids, ion permeability, and absolute temperature
• The amounts of cations and anions are balanced on both sides of the membrane at approximately 150 mmol/l each
• Under resting conditions, there is a slight excess of anions on the inner side and cations on the outer side of the membrane
• The potential is primarily due to ion diffusion through the semipermeable membrane and is modified by the Na-K-ATPase.
• The composition of ECF and ICF is different
• The membrane is 50-100 times more permeable to K+ than to Na+
• Intracellular fixed anions (proteins) exist
• Na-K-ATPase is present

Electrochemical Equilibrium Potential

• Electrochemical equilibrium is achieved when the electrical and chemical forces acting on an ion are equal and opposite, resulting in no net movement of the ion across the membrane
• The electrochemical equilibrium potential is the membrane potential at which this equilibrium occurs for a particular ion

Nernst Equation

• The Nernst equation calculates the equilibrium potential for a specific ion based on its concentration gradient across the membrane
• The equation is:
  • Ex = (-R * T) / (n * F) * ln([X]i / [X]e)
  • Where:
    • Ex is the equilibrium potential for ion X
    • R is the gas constant (8.314 J.K-1.mol-1)
    • T is the absolute temperature in Kelvin (K = °C + 273.15)
    • n is the ion valency
    • F is the Faraday constant (96485 C.mol-1)
    • ln is the natural logarithm
    • [X]i is the intracellular ion concentration
    • [X]e is the extracellular ion concentration
• A simplified version for n = +1 and T = 310.15 K is Ex = ±61 * log([X]i / [X]e)
  • Use - for cations and + for anions
  • log is the decadic logarithm (log10x)

Examples of Ion Equilibrium Potentials

• For an artificial membrane permeable only to K+:
  • Intracellular K+ concentration (Ki) is 140 mmol/l
  • Extracellular K+ concentration (Ke) is 4 mmol/l
  • The calculated equilibrium potential (EK) is -94 mV
• For an artificial membrane permeable only to Na+:
  • Intracellular Na+ concentration (Nai) is 10 mmol/l
  • Extracellular Na+ concentration (Nae) is 145 mmol/l
  • The calculated equilibrium potential (ENa) is +71 mV
• For an artificial membrane permeable only to Cl-:
  • Intracellular Cl- concentration (Cli) is 5 mmol/l
  • Extracellular Cl- concentration (Cle) is 100 mmol/l
  • The calculated equilibrium potential (ECl) is -79 mV
• For an artificial membrane permeable only to Ca2+:
  • [Ca2+]i is 10^-4 mmol/l
  • [Ca2+]e is 1.2 mmol/l
  • The calculated equilibrium potential (ECa) is +124 mV

Driving Potential

• The driving potential is the difference between the membrane potential and the equilibrium potential for an ion
• It represents the force driving an ion across the membrane
• For K+:
• [K+]i is 140 mmol/l
• [K+]o is 4 mmol/l
• Calculated EK is -94 mV
• If the membrane potential (EM) is -80 mV, then the driving potential is: U = |EM – EK| = 14 mV
• For Na+:
• [Na+]i is 10 mmol/l
• [Na+]e is 145 mmol/l
• Calculated ENa is +71 mV
• If the membrane potential (EM) is -80 mV, then the driving potential is: U = |EM - ENa| = 151 mV

Membrane Current

• Membrane current (Ix) is determined by Ohm's law and the driving potential
• I = U/R, where I is current, U is voltage, and R is resistance
• I = U * g, where g is electrical conductance (inverse of resistance)
• Driving potential is EM - Ex, where EM is the membrane potential and Ex is the equilibrium potential of ion X
• Ix = gx * (EM – Ex)
• Where:
  • Ex is the electrochemical equilibrium potential of ion X
  • g is the electrical conductance
  • EM is the membrane potential

Permeability and Membrane Potential

• When an artificial membrane is permeable to both K+ and Na+ the membrane potential (EM) depends on the relative permeability of each ion
• If permeability to K+ is 1 and to Na+ is 0, then EM = EK = -94 mV
• If permeability to K+ is 1 and to Na+ is 0.01, then the overall membrane potential shifts slightly towards the sodium equilibrium potential, resulting in Em being -84 mV
• If permeability to K+ is 1 and to Na+ is 0.05, then overall membrane potential shifts more towards the sodium equilibrium potential, resulting in Em being -70 mV
• If permeability to K+ is 1 and to Na+ is 1, the membrane potential is -11mV
• If permeability to K+ is 0 and to Na+ is 1, then EM = ENa = +71 mV

Ion Concentrations

• Ion concentrations (mmol/l) in the extracellular fluid (ECF) and intracellular fluid (ICF):
  • Na+: ECF: 145, ICF: 10
  • K+: ECF: 4, ICF: 140
  • Ca2+: ECF: 1.2, ICF: 10^-4
  • Mg2+: ECF: 0.5, ICF: 1
  • Cl-: ECF: 100, ICF: 5
  • HCO3-: ECF: 25, ICF: 10
  • A- (remaining anions): ECF: cca 26, ICF: cca 135

Goldman-Hodgkin-Katz (GHK) Equation

• The Goldman-Hodgkin-Katz equation calculates the membrane potential considering the permeability and concentration gradients of multiple ions
• The equation is:

  Em = (RT / F) * ln ( (pk[K+]o + pNa[Na+]o + pCl[Cl-]i) / (pk[K+]i + pNa[Na+]i + pCl[Cl-]o) )
  Where:
  - Em is the membrane potential
  - R is the gas constant
  - T is the absolute temperature
  - F is the Faraday constant
  - pk, pNa, pCl are the relative permeabilities of potassium, sodium, and chloride ions
  - [K+]o, [Na+]o, [Cl-]o are the extracellular concentrations of potassium, sodium, and chloride ions
  - [K+]i, [Na+]i, [Cl-]i are the intracellular concentrations of potassium, sodium, and chloride ions

• In a real cell, typical values are:
  • [Na+]e = 145 mmol/l
  • [Na+]i = 10 mmol/l
  • [K+]i = 140 mmol/l
  • [K+]o = 4 mmol/l
  • [Cl-]i = 5 mmol/l
  • [Cl-]e = 100 mmol/l
  • pK = 1
  • pNa = 0.05
  • pCl = 0.45
• Using these, EM = -70 mV

Membrane Reaction to Stimulation

• If a membrane has voltage-gated ion channels and the stimulus is strong enough
• An action potential occurs, exclusively on excitable membranes
• If a membrane lacks voltage-gated ion channels or the stimulus is insufficient
  • A graded potential develops (passive, electrotonic response) on all cell membranes and excitable membranes after a subthreshold stimulus
  • Graded responses have names such as: IPSP, EPSP, end-plate, receptor, local response

Electrotonic (Graded) Potential

• Graded potentials can be either depolarizing or hyperpolarizing
• They are localized changes in the membrane potential that vary in magnitude depending on the strength of the stimulus

Action Potential

• Action potentials occur on excitable membranes (nerve, muscle: skeletal, cardiac, smooth)
• Action potentials are stereotyped responses
• Action potentials transport information via propagation

Characteristics of Action Potentials

• Threshold:
  • Membrane potential value needed to generate an AP, opening Ina channels
• Threshold, Above-Threshold Stimulus:
  • Electrical response with a set amplitude and duration = all-or-none response
  • No AP occurs if the threshold is not reached
  • A stereotyped AP is generated if the threshold is reached or exceeded
  • AP propagates through the membrane, remains consistent, and spreads without decrement
• Refractoriness:
  • Insensitivity to further immediate stimulation on excitable membranes
• Absolute Refractory Period
  • The membrane cannot generate another AP, regardless of stimulus intensity
  • Starts after AP initiation and covers nearly the entire AP duration
• Relative Refractory Period
  • Immediately follows the absolute refractory period
  • A greater stimulus is needed to reach the threshold
  • Observed at the end of AP (INa recovery) and during after-hyperpolarization (increased IK conductance)

Non-Excitable Membrane

• Found in postsynaptic regions, dendrites, neuronal somata, and receptors
• Cannot generate action potentials
• Exhibits electrotonic propagation with decrement
• Electrical response is proportional to stimulus intensity, known as a graded response

Local vs. Action Potentials

Propagation of Graded Potential

• Passive spread with decrement, the change in membrane voltage decreases with distance from stimulation site
• Response amplitude depends on stimulus intensity
• Distance of propagation depends on stimulus intensity and membrane characteristics (membrane resistance RM and axoplasm resistance RA)
• The distance is: Vx = V0 * e^(-x/λ)
  • V0 is the voltage change at point 0
  • Vx is the voltage change at point x
  • x is the distance from point 0
  • λ is the length constant
  • A = Sqrt(RM/RA)
• Electrical current applied at point 0 leads to charge distribution changes
• This causes a localized membrane voltage change at point 0
• Applied charge moves along the fiber's axis relative to axoplasm resistance
• Greater resistance (smaller fiber diameter) limits charge transport
• Some charge returns to the ECF through ion channels
• A smaller and smaller charge subsequently reaches more distant areas of the fiber and the voltage change decreases with distance
• The length constant increases when membrane resistance increases, stopping charge from escaping and decreases with axoplasm resistance
• Electrotonic responses and electrical currents from voltage change only spread short distances and usually disappear within 1-2 mm

Propagation of Action Potential

• Depolarization at a point causes membrane transpolarization
• A voltage difference between adjacent membrane segments causes local currents to carry positive charges in the propagation direction (Na+ diffusion)
• Depolarization spreads to neighboring regions
• The adjacent membrane segments threshold value is reached and an AP is generated

Direction of Propagation

• If membrane properties are constant
  • AP is the same everywhere, spreading without decrement
• Adjacent sections of membrane affect each other electrotonically
• Propagation velocity depends on the length constant and the speed of propagation
• Larger fiber diameter reduces the RA and increases the length constant and the velocity of propagation.
• The (A = Sqrt(RM/RA))
• On isolated nerve fibers.
  • Velocity of propagation is the same in both directions
• If an AP is triggered at any site of the axon
  • AP propagates in both directions (electrotonic spread)
• Physiologically, AP propagation is orthodromic
  • Initial axon segment(axon hillock) has the lowest threshold
  • Refractoriness prevents impulse from propagating antidromically

Propagation of Action Potential in Myelinated Membrane

• Myelin sheath electrically insulates the nerve fiber (Schwann cells in PNS, oligodendroglia in CNS)
• The nodes of Ranvier are the only site of contact between the axolemma and the ECF
• Myelin sheath substantially increases RM and the length constant
• APs are generated exclusively in the nodes of Ranvier where there is high density of ion channels
• High RM leads to the signals traveling long distances
• Long distance propagation of the electrotonic impulses leads to above-threshold depolarization in the neighboring node of Ranvier resulting in an AP
• Myelinated segments are excluded from AP generation (high resistance, no/low density relevant channels)
• AP appears to jump from one node to the next (saltatory conduction)
• Length constant is long enough for impulse conduction over several myelinated segments
• Elimination of myelinated segments from electrogenic processes leads to:
  • Energy-saving (lower # of exchanged ions)
  • Faster conduction (AP generation in Ranvier node is the slowest process)

Classification of Nerve Fibers

• Afferent (sensory) carry signals from receptors to CNS
• Efferent (motor) carry signals from CNS to effectors
• Interneurons connect afferent and efferent neurons