Question

A membrane consists of \(50 \%\) protein by weight and \(50 \%\) phosphoglycerides by weight. The average molecular weight of the lipids is 800 Da, and the average molecular weight of the proteins is 50,000 Da. Calculate the molar ratio of lipid to protein.

Short answer

The molar ratio of lipid to protein is 62.5.

Step-by-step solution

Define Given Information

Identify and define all the given values: the weight percentages and molecular weights. The membrane is 50% protein and 50% lipid by weight. The average molecular weight of the lipid is 800 Da and the average molecular weight of the protein is 50,000 Da.

Convert Weight Percentages to Grams

Let's assume we have 100 grams of the membrane for simplicity. This means we have 50 grams of protein and 50 grams of lipid.

Calculate Moles of Lipids

Use the formula \( \text{moles} = \frac{\text{mass}}{\text{molecular weight}} \) to calculate the moles of lipids. Using the given values: \( \text{moles of lipids} = \frac{50 \text{ g}}{800 \text{ Da/g}} = 0.0625 \text{ moles} \).

Calculate Moles of Proteins

Similarly, calculate the moles of proteins: \( \text{moles of proteins} = \frac{50 \text{ g}}{50000 \text{ Da/g}} = 0.001 \text{ moles} \).

Find the Molar Ratio

The molar ratio of lipid to protein is found by dividing the number of moles of lipids by the number of moles of proteins: \( \text{Molar Ratio} = \frac{0.0625}{0.001} = 62.5 \).

Key concepts

Membrane Composition

The composition of a cell membrane plays a critical role in its function and structure. Membranes are typically made up of lipids and proteins. In the given exercise, the membrane consists of equal parts of protein (50%) and phosphoglycerides (50%), both by weight. Proteins are responsible for various functions such as transport, signaling, and structural support. Lipids, specifically phosphoglycerides, form the bilayer structure, providing a semi-permeable barrier.

Molecular Weight

Molecular weight refers to the mass of a given molecule and is often measured in Daltons (Da). In this exercise, we know that the average molecular weight of the lipid molecules is 800 Da, while the proteins have a significantly higher average molecular weight of 50,000 Da. This is important for calculating the molar ratio because it gives us a bridge between mass (grams) and amount of substance (moles). By converting between these units using molecular weight, we can understand the quantity of molecules present.

Molar Ratio

The molar ratio is a way to compare the amounts of different substances in a mixture. It's expressed as the ratio of the number of moles of one substance to the number of moles of another. In this exercise, we need to find the molar ratio of lipids to proteins. By assuming the membrane weight is 100 grams (50 grams each of lipid and protein), we convert these weights into moles using their respective molecular weights: \[ \text{moles of lipids} = \frac{50 \text{ g}}{800 \text{ Da/g}} = 0.0625 \text{ moles} \ \text{moles of proteins} = \frac{50 \text{ g}}{50000 \text{ Da/g}} = 0.001 \text{ moles} \ \text{Molar Ratio} = \frac{0.0625}{0.001} = 62.5 \] This means there are 62.5 moles of lipid for every mole of protein.

Lipids

Lipids are hydrophobic or amphiphilic small molecules that include fats, waxes, sterols, and phosphoglycerides, among others. They form the structural foundation of cell membranes. In the membrane, they arrange themselves into a bilayer, with hydrophobic tails facing inward and hydrophilic heads facing outward. This arrangement creates a permeable barrier essential in various cellular processes. In this exercise, the lipids involved are phosphoglycerides, which have an average molecular weight of 800 Da.

Proteins

Proteins are large, complex molecules made up of amino acid chains. They perform a vast array of functions within biological organisms, including catalyzing metabolic reactions, DNA replication, and transporting molecules. Proteins in the membrane help in signaling and structural support and serve as channels or pumps to move substances across the cell membrane. In our calculations, the average protein molecular weight is 50,000 Da, showing how much larger and more complex these molecules can be compared to lipids.