# Unfolded Protein Equilibrium (BIO)

In this example we are given the total protein

concentration in solution, it’s 10 micromolar, and the question we ask is what fraction

of this protein is unfolded at 25 degree C? where we are given the delta G of unfolding

and this value then of course is at 25 degrees C. So what we are looking at is, there is

a folded version of the protein, and it is in equilibrium with an unfolded version, and

the question really is what fraction or what is the concentration that is unfolded. So

we will use the notation were N represents the concentration of folded, and U represents

the concentration of unfolded , and the problem says that the sum of the two types is the

concentration of 10 micromolar. So ten to the minus six molar concentration. So this

is an equilibrium process. We are given delta G, which means we can calculate the equilibrium

constant, and then we’re going to say the equilibrium constant is equal to the concentration of the unfolded. The product over the folded,

and we can use concentrations here, These are low concentrations so we are treating this as

ideal. The equilibrium constant is equal to the Gibbs free energy change divided by the

gas constant and the temperature. So we can calculate the equilibrium constant because

we are given delta G, minus sign. This is 41000 Joules per mole. the gas constant 8.314 Joules per mole per Kelvin. So this temperature must be absolute temperature 273 plus 25 so 298 Kelvin. This is equal to then e to the minus 16.55. So if we do that exponential we get a very small equilibrium constant not

surprising we have a positive delta G that is significant in size, and so our equilibrium

calculation is just that U over N is 6.5 times ten to the minus eight Essentially we can stop here. Essentially

what this says is that essentially there is no unfolded protein. Such a small fraction

of the total if we wanted to calculate the concentration, and then since N is pretty close to

ten to the minus six molar then U is equal to ten to the minus six times 6.5 times ten to the minus eight. So our concentration is 6.5 times ten to the minus fourteen molar. This is the concentration of the unfolded protein, and so this really is insignificant, and we conclude for these conditions, this temperature, all the protein is folded.