Calculate the Delta G for the following scenarios and state

Calculate the Delta G for the following scenarios and state which require energy to happen. Show your calculations. The internal potassium (K+) concentration is 30x greater than the external concentration. For a cell at 37C with no membrane potential, what is the Delta G? The internal potassium (K+) concentration is 30x greater than the external concentration. For a cell at 37C with a membrane potential of -60mV, what is the Delta G? The internal chloride ion (CI^-) concentration is 12mM and the external concentration is 145mM. For a cell at 25C with a -90mV membrane potential, what is the Delta G? The internal pH is 8.0 and the external pH is 7.0. For a cell at 25C with a -180mV membrane potential, what is the Delta G for the proton gradient?

Solution

4. a

A concentration of K+ inside the cell is 30X more than outside.

a body temperature of 37°C, so an absolute temperature of 37 + 273 = 310°K, and

G = RT ln( X in / X out)          

G = the change in free energy

R = 2 ( gas constant)

T = K , absolute temperature = C + 273

Ln = natural log

Xin = internal ion conc

X out = external ion conc

Therefore

G = (2)(273+37) x ln (30x/1x)

= (2)(310) x ln (30)

= (620)(3.4) = +2108 cal/mole

= +2.1 kcal/mole

Since the G is positive, it requires energy.

4b. This time we have membrane potential. = -60mV

G = (R)(T) x ln(30x/1x) + (z)(F)(V_m)

     = (2)(273+37) x ln (30) + (+1)(23,062)(-0.06)

     = (620) x (3.4) + (-1387)

   =+ 721cal /mol

= + 0.721 Kcal/ mol

Since the G is positive, it requires energy to transport.

4c. X out = 145mM

X in = 12mM

T = 25C

V= -90mV

Z = -1

G = (2)(273+25) x ln (12mM / 145mM) + (-1)(23,062)(-0.09)

= 596 X (-2.52) + (2075)

= -1501 + 2075

G = +573.

Since the G is positive, it requires energy to transport.

4d.

G = - 2.303 RT pH + (z)(F)(V_m)===> (NOTE: DpH = pHin - pHout )

= -2.303 (2)(273+25) + (+1) (23,062) (-0.180)

= -1372 + (-4151)

= - 5523cal /mol

=-5.5Kcal/mol

Since the G is negative, the reaction is spontaneous.