Question

Calculate the V_m of a cell that is permeable to sodium and potassium at 22 degrees Celsius. What is the effect of the temperature on the V_m of the cell? Hint need to look up information on the Nernst equation in order to solve this.​

P_k = 100, P_{Na = 5,} P_Cl = 10, P_Ca = 1

Extracellular conc. of potassium: 5 mM

Extracellular conc. of sodium: 150 mM

Intracellular conc. of potassium: 100 mM

Intracellular conc. of sodium: 15 mM

NOTE THAT THE CELL IS PERMEABLE TO SODIUM & POTASSIUM​. Also, would you or would you not take the ratio for the sodium-potassium pump into consideration?

Answer 1

Vm is the equilibrium membrane potential is exactly equal and opposite to the diffusive forces of ions ,so that no net flow of ions occurs in and out of the cell membrane.This value depends only on the concentration of ions inside and outside the cell membrane.The ratio of sodium and potassium pump is taken into consideration in Vm calculations.

goldmann-hodgkin-katz equation to calculate Vm:

Vm=RT/F ln( (PK [K]out+PNa [Na]out +PCl[Cl]in+PCa[Ca]out)/(PK [K]in+PNa [Na]in +PCl[Cl]out+PCa[Ca]in))

where R=universal gas constant=8.314 J/K.mol

T=temperature =22+273=295K

F=faraday's constant =96485 C/mol

Pi represents the permeability of ion i

[ION}out =concentration of ion outside

[ION]in =concentration of ion inside

Vm=(8.314J/Kmol)*295K/ (96485 C/mol) ln( (100 *5mM+5* 150mM )/(100 *100mM+5* 15mM)) [As Cl- is not actively pumped ,it hardly affects Vm )

Vm=0.0254V ln (1250mM/10075mM)=-0.053V

Vm=-0.053V