Human Physiology: Membrane Potential

Membrane Potential

what is a membrane potential?

- membrane potential: difference in voltage across a membrane; normally negative under resting conditions

- values

- mammalian skeletal muscle: -90 mV

- mammalian neurons: -60 to -80 mV

- change from resting

- hyperpolarized: more negative than the resting potential

- depolarized: more positive than the resting potential

development of the membrane potential: electrochemical gradient

- electrochemical gradient: interaction of diffusion and charge gradients

- ion concentration gradients: arise through active transport of ions by membrane pumps and carriers

- Na⁺/K⁺ ATPase: utilizes ATP to establish Na⁺ and K⁺ ionic concentrations

- net effect: higher extracellular Na⁺, higher intracellular K⁺

- electrical gradients: arise through selective permeability of membrane to K⁺

- Na⁺ is transported out of the cell, and K⁺ is transported in

- under resting conditions, the cell is permeable to K⁺, and some small amount of K⁺ diffuses out

- net effect: loss of K⁺ ions, creating a net negative charge on the internal surface of the membrane

- equilibrium potential: balance between the diffusional and charge forces

- mechanism: K⁺ gradient

- diffusion pushes K⁺ out, building up a net external positive charge

- because of charge repulsion, this electrical gradient opposes the diffusional gradient

- equilibrium potential is established when electrical and chemical gradients are balanced

- equilibrium potential: each ion has one, based on permeability and concentration differences

- E_K ≈ -90 mV

- E_Na ≈ +65 mV

- systemic characteristics

- permeable charged solute does not equilibrate to equal concentrations due to the electrical repulsion

- total number of charges that cross the membrane is small (no large scale redistribution of [ion])

- summary

- membrane potential (E_m): formed by slight intracellular cation excess and extracellular anions excess

- bulk electroneutrality: potential develops without large redistribution of ions

- resting potentials: range from -5 mV to -100 mV in different cells

- neurons and myocytes: -50 mV to -90 mV

- directionality: by convention, membrane potential refers to potential inside cell with respect to ground

the Nernst potential, E_ion

- calculation of equilibrium potential: the Nernst equation

- Nernst equation:

- R: universal gas constant

- T: temperature (K; body temperature = 37 ºC = 310 K)

- z_ion: ionic valence (e.g. z_Cl = -1, z_Ca = +2)

- F: Faraday’s constant

- [C]_o: extracellular ion concentration

- [C]_i: intracellular ion concentration

- important equilibrium potentials

- K⁺:

- Na⁺:

- Cl^-:

- mechanisms responsible for generating the resting membrane potential

- Na⁺/K⁺ ATPase

- direct: nonsymmetrical movement of ions small (<20%)>rest

- indirect: maintenance of Na⁺ and K⁺ gradients majority of E_rest

- passive efflux of K⁺

- outward [K⁺] gradient: maintained by Na⁺/K⁺ ATPase

- inward electrical gradient: results from K⁺ diffusion through ion channels

- E_K = - 90 mV

- passive influx of Na⁺

- inward [Na⁺] gradient: maintained by Na⁺/K⁺ ATPase

- outward electrical gradient: results from Na⁺ diffusion through ion channels

- E_Na = + 61 mV

- summary: establishing a negative resting membrane potential

- Na⁺/K⁺ directly (electrogenically) creates only about 20% of the resting membrane potential

- the remaining 80% results from K⁺ efflux and Na⁺ influx

- passive conductance of K⁺ is much greater due to the greater number (50-75 X) of open K⁺ channels at rest

- K⁺ thus has a larger influence on E_m, and thus E_m is much closer to E_K

- origin of the Nernst equation

- electrochemical potential of an ion:

- Δμ: electrochemical potential difference of the ion between compartments

- Ψ_i - Ψ_o: V_m; electrical potential difference across the membrane

- contributions of the concentration gradients and potential difference

- concentration gradient:

- charge separation:

- Nernst equation: equilibrium potentials

- positive Δμ: net drive of positive ions outward

- negative Δμ: net drive of positive ions inward

- Δμ = 0: ion movement at equilibrium

- Nernst equation derived by setting Δμ = 0, solving for V_m

the resting potential

- resting potential

- Nernst (equilibrium) potential: voltage at which an individual ionic species is at electrochemical equilibrium

- resting potential: voltage at which there is no net flux of charge across the membrane

- main determinant: charge separation by K⁺ movement

- minor determinant: electrogenic properties of Na⁺/K⁺ ATPase

- the Goldman-Hodgkin-Katz (GHK) constant field equation

- GHK equation:

- function: predicts changes in V_m when net current across membrane is zero (at rest)

- ↑ numerator: more negative V_m

- ↓ numerator: more positive V_m

- ↑ denominator: more positive V_m

- ↓ denominator: more negative V_m

- P_ion: relative permeability of the ion

- permeability

- somewhat analogous to conductance, though the concepts are not identical

- varies with V_m (since probability of channels being open varies with V_m)

- alteration of serum K⁺ can dramatically affect membrane excitability

- hyperkalemia: increased extracellular potassium, depolarizing membrane potential

- hypokalemia: decreased extracellular potassium, hyperpolarizing membrane potential

- the chord conductance equation

- permeability vs. conductance

- permeability: chemical concept, measuring the relative likelihood of ions being able to cross a membrane

- conductance: electrical concept, relating charge movement to driving force on the charges

- current equations

- Ohm’s law:

- conductance:

- current: one ion

- current: multiple ion sum

- chord conductance

- equation:

- derivation: resting potential assumes I_total = 0, so set I to zero and solve for V_m

- consequences

- conductance ratios are fractions of the total conductance, where g_total = g_K + g_Na + g_Cl

- as conductance to a given ion increases, its contribution to V_m also increases

- opening more of any type of ion channel will cause V_m to move toward that ion’s equilibrium potential

- role of the Na⁺/K⁺ ATPase in development of resting membrane potential

- direct: due to ion transport stoichiometry of 3 Na⁺ : 2 K⁺, causing slight hyperpolarization (<5>

- indirect: due to outward diffusion of K⁺ at rest

- maintenance: slow leak of Na⁺ and K⁺ is offset, thus maintaining the ion gradient

changes in membrane potential

- theory

- membrane potential: results from unequal separation of charge across a membrane

- changing current does not instantly change V_m due to the required time for charge movement

- time dependence: resistance and capacitance

- total current:

- resistance current (Ohm’s law):

- capacitance current (empirical):

- time dependence: rate of change of voltage

- voltage change:

- consequences

- as conductance increases (resistance decreases), the rate of voltage change will increase

- as capacitance increases, the rate of voltage change will decrease

- simple case: spherical cell

- time constant:

- steady state V_m:

- summary

- membrane potential tends towards equilibrium

- equilibrium potential is a weighted average of permeable ion equilibrium potentials

- opening specific ionic channels draws V_m­ towards the E_ion

- opening ionic channels reduces R_m, increasing conductance and reducing the time constant (τ)