Question

Questions: 1. Nerves: Get your calculators out! As expected, you are about to experience the deep satisfaction of solving the Goldman equation to predict the axon membrane potential, as presented in your book and lecture notes. Nernst (cations only): V (MV) = 61 log(CIC) P Na+PK)-PaC). Goldman: V (mV) = 61 log P [Na]. + P (K). + PCI)- To solve this equation, you will need to use the following concentrations inside (i) and outside (o) the cell and permeabilities (P) of sodium (Na), potassium (K) and chloride (CI) for the neuron: K. = 5 (all) K = 150 Na, = 150 Na = 15 CI, = 125 CI = 9 Pa = 109, Pk = 108 Pa = 10 (All concentrations in mM and permeabilities are in units of cm/s but see "hints" below) 1) First, what is the Nernst Potential for each of the three ions? (3 points) 2) Second, assuming that the above given values represent reasonable conditions for the "resting axon", solve the Goldman equation to predict the resting membrane potential of this cell. (2 point)

Answer 1

Answer 1:)

Nernst potential for Na ions:

Vm(Na) = 61 log Na_O/Na_i

Vm(Na) = 61 log 150/15

Vm(Na) = 61 log 10

Vm(Na) = +61 mV

Nernst potential for K ions:

Vm(K) = 61 log K_O/K_i

Vm(K) = 61 log 5/150

Vm(K) = 61 log 0.1

Vm(K) = -61 mV

Nernst potential for Cl ions:

Vm(Cl) = 61 log Cl_O/Cl_i

Vm(Cl) = 61 log 125/9

Vm(Cl) = 61 log 13.9

Vm(Cl) = 61 x 1.14

Vm(Cl) = 69.54 mV

Answer 2:)

By using the given Goldman equation, the membrane potential is below:

10-'150] + 10-8[5] + 10-99) Vm = 611og7 10-9/15] + 10-8150] + 10-9[125]

15 x 10-8 + 5 x 10-8 +0.9 x 10-8 "1.5 x 10-8 + 150 x 10-8 + 12.5 10-8

10-8(15+5 +0.9) Vm Vm = 61log 10-877 0 9 10-8(1.5 + 150+ 12.5)

20.9 Vm = 611092103

V_m = 61 x (-0.9)

V_m = -55 mV (nearly)

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