Question

Transport of ions in the organ of Corti in the inner ear. The organ of Corti (OC) has highly specialized structures that respond to fluid-borne vibrations in the cochlea with a shearing vector in the hairs of some cochlear hair cells. The cochlear partition that includes the OC is placed between two fluid-filled ducts, the scala media and the scala tympani. The scala media maintains a high K+ (140 mM) and low Ca2+ (5 × 10-6 mM) endolymph, while the scala tympani contains perilymph with abundant Ca2+ (1.8 mM). In addition, there is -90 mV electric potential between the two compartments. If 1:1 sym-transport of K+ ions is used as the only means to transfer the Ca2+ ions from the scala media to the scala tympani, predict the concentration of K+ in the scala tympani.

Answer 1

Scala Tympani has Ca²⁺ = 1.8 mM, K⁺ =?

Scala Perilymph has Ca²⁺ = 5 x 10^-6 mM, K⁺ = 140 mM

Electric Potential between the two, scala tympani and scala perilymph = -90 mV

Therefore, to calculate the ion concentration from the electric potential, Goldman-Hodgkin-Katz (GHK) equation can be used:

E_m= -RT/F log [P_k [K]_in + P_Ca [Ca]_in/ P_k[K]_out + P_Ca [K]_out

Similarly, Nernst Equation can be used, according to which:

V = RT/zF In [K _out/K_in]

Here, R is the Universal gas constant and is 8.314 JK^-1mol^-1, z is the valence of K and is +1, F is the faraday constant and is 96,485 C mol^-1

-90 mV = 8.314 JK^-1mol^-1/ +1 x 96,485 Cmol^-1 In [K_out/140]

-90 mV = 8.314 JK^-1/96,485 C In [K_out/140]

-90 mV x 96,485 C/ 8.314 JK^{-1 =} In [K_out/140]

8683650/8.314 = K_out/140

K_out = 72195866.1/140 = 5156817 = 515 mM