A student believes that a protein she has isolated binds...

A student believes that a protein she has isolated binds zinc. The protein has a molecular weight of 102,000 . She performs a dialysis equilibrium experiment in which the concentration of protein within the bag is $1 \mathrm{mg} / \mathrm{ml}$. The bag is equilibrated with a large concentration inside the bag at equilibrium yields $0.12 \mathrm{mM}$. How many $\mathrm{Zn}$ ions are bound per molecule of protein?

Key Concepts

Molecular Weight to Molarity Conversion

Converting a protein’s concentration from mass per volume (mg/ml) to molarity is a fundamental technique in biochemistry. This conversion, which uses the protein’s molecular weight, is crucial for calculating the number of moles (and hence molecules) present in a solution, enabling accurate determination of binding ratios with ligands.

Protein-Ligand Binding Stoichiometry

This concept involves determining the ratio in which ligands (in this case, metal ions such as zinc) bind to a protein. It is important to understand how many ligand molecules associate with each protein molecule, which can provide insights into the protein’s structure and function.

Dialysis Equilibrium Technique

Dialysis equilibrium is an experimental method used to separate molecules based on size and to study binding interactions. In the context of binding studies, it allows researchers to determine the concentration of free and bound ligands by equilibrating a protein solution with an external solution, thereby facilitating the calculation of binding stoichiometry under equilibrium conditions.

Transcript

00:01 For this question, we have the data for the osmotic pressure of a solution containing a protein, and we have to compute the molar mass of that protein.

00:11 So first, let's work out an equation that will let us to compute this molar mass.

00:17 So we know that the osmotic pressure is computed by the product of concentration, gas constant, temperature, and the vanhoff factor.

00:30 Okay, however, we also know that the concentration is just the number of moles divided by the volume.

00:38 So let's plug this in here.

00:40 So we can rewrite this as number of moles over volume times r, t.

00:49 Now, we also, we don't have the number of moles.

00:54 What we have is the mass, and we want to find a molar mass.

00:58 So let's recall that the number of moles is computed by taking.

01:01 In the mass which i'm represented by little m this is mass normalality in this context and you divide that by the molar mass so for the molar mass i'm gonna use a capital m with a bar molar mass okay all right so we can also plug this in here so we have a new equation now in terms of mass okay volume and molar mass great so we have we have everything here.

01:35 We have the osmotic pressure, we have the mass, the volume, gas constant temperature, and we want the molar mass.

01:42 So let's rewrite this equation, but having just m bar in the one side, in the left side.

01:54 Okay? let's isolate this variable.

01:58 And we will have m r t i over the pi.

02:05 That's our formula.

02:08 That's how you can find molar mass from an osmotic pressure experiment.

02:17 So all we have to do now is to plug in numbers.

02:21 All right.

02:24 So the molar mass will be equal.

02:28 So the mass is 2 to 5 grams.

02:33 The gas constant will be 0 .082 in this case.

02:39 Atm, liters, kelvin, let me write this way, per kelvin, per mole, okay, so those are the units for r.