If resting membrane potential of a cardiac cell is -90mV, the concentration of K^+ outside the cell is 5mM and membrane permeability for all cations (except forK^+) is zero. What is the concentration of K^+ inside of the cell?

Problem 1

If resting membrane potential of a cardiac cell is -90mV, the concentration of K^+ outside the cell is 5mM and membrane permeability for all cations (except forK^+) is zero. What is the concentration of K^+  inside of the cell?

Answer: 

Given data; 

Resting membrane potential of a cardiac cell =-90mV

Concentration of K^+  outside the cell = 5mM

Concentration of K^+   inside of the cell?

E_(m,K^+ )=RT/F ln⁡([K^+ ]_out/[K^+ ]_in 

E_(m,K^+ )=61.5mVln⁡([K^+ ]_out/[K^+ ]_in 

-90mV=61.5mV ln⁡([5mM]_out/[K^+ ]_in 

(-90mV)/(61.5mV.⁡)=ln [5mM]_out/[K^+ ]_in 

1.46mV=ln [5mM]_out/[K^+ ]_in 

0.3784=[5mM]_out/[K^+ ]_in 

[K^+ ]_in=[5mM]_out/0.3784

[K^+ ]_in=13.21mM

Concentration of K^+  inside the cell = 13.21mM

Problem 2

 The internal concentration of K^+ in a cell is 150mM, and the cell’s diameter is 10μm. If resting membrane potential of the cell is -50mV, and the capacitance of the cell membrane is 0.5 μF/cm2, what is the surface density of K^+  needed to produce the resting membrane potential? (HINT: Wikipedia has a good explanation and definition of capacitance.)

Solution 

Internal concentration of K^+  in a cell =  150mM

Cell’s diameter =10μm=0.5×10^(-6)

Membrane potential of the cell is = -50mV

Capacitance of the cell membrane =  0.5 μF/cm^2 =0.5×10^2 F/m^2

What is the surface density of K^+= ? 

Charge density is σ=cv= -0.5×0.5×10^(-2) c/m^2  

Charge density is σ=0.25×10^(-2)   c/m^2 

σ_max=2.5×10^(-4)  c/m^2   

σ_(K^+ )= 2.5×10^(-4)  c/m^2 ×150×10^(-3)  c/m^2 

σ_(K^+ )= 3.75×〖10〗^(-5)  c/m^2