Question

Molecular Species in the Plasma Membrane The plasma membrane of \(\mathrm{E}\). coli is about \(75 \%\) protein and \(25 \%\) phospholipid by weight. How many molecules of membrane lipid are present for esch molecule of membrane protein? Assume an average protein \(M_{\text {, of }} 50,000\) and an average phospholipid \(M_{\mathrm{r}}\) of 750 . What more would you need to know to estimate the fraction of the membrane surface that is covered by lipids?

Short answer

There are approximately 22 lipid molecules per protein molecule. To estimate surface coverage, we need the size of each molecule.

Step-by-step solution

Understand the Problem

We need to find the ratio of lipid molecules to protein molecules in the membrane of E. coli. Given is the percentage by weight of proteins and phospholipids in the membrane, along with their average molecular weights.

Determine Relative Mass Contribution

The mass contribution of proteins in the membrane is 75% and of phospholipids is 25%. This means for every 100g of membrane, there are 75g of protein and 25g of phospholipids.

Calculate the Number of Moles of Protein

Using the formula for moles, \( \, \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), the moles of protein \(= \frac{75 \text{ g}}{50,000 \text{ g/mol}} = 0.0015 \text{ mol} \).

Calculate the Number of Moles of Phospholipid

Similarly, the moles of phospholipid \(= \frac{25 \text{ g}}{750 \text{ g/mol}} = 0.0333 \text{ mol} \).

Determine Molecule Ratio

The ratio of lipid molecules to protein molecules is \( \frac{0.0333 \text{ mol}}{0.0015 \text{ mol}} = 22.2 \). Therefore, there are approximately 22 molecules of lipid for each molecule of protein.

Information Needed for Surface Area Coverage

To estimate the fraction of the membrane surface covered by lipids, we would need to know the surface area taken up by a single phospholipid molecule and a protein molecule. This includes their size and the arrangement in the membrane.

Key concepts

Phospholipid Molecule Ratio

The plasma membrane's composition involves both proteins and phospholipids, which differ significantly in their amounts by weight. To find the ratio of phospholipid molecules to protein molecules in the membrane, consider the given weight percentages. Proteins make up 75% of the weight, while phospholipids account for 25%. This means, for every 100 grams of the membrane, there are 75 grams of protein and 25 grams of phospholipids.

To find the number of molecules, we first convert these masses into moles using their molecular weight. The molecular weight of an average protein is given as 50,000 g/mol and that of a phospholipid as 750 g/mol. For proteins, the moles per 100g membrane is calculated as \( \frac{75\text{ g}}{50,000\text{ g/mol}} = 0.0015\text{ mol} \). Correspondingly, phospholipids are \( \frac{25\text{ g}}{750\text{ g/mol}} = 0.0333\text{ mol} \).

The ratio of lipid molecules to protein molecules can be determined by dividing the number of moles of lipids by the number of moles of proteins \( \frac{0.0333\text{ mol}}{0.0015\text{ mol}} \approx 22.2 \). Thus, for each protein molecule, there are approximately 22 phospholipid molecules.

Molecular Weight Calculation

Calculating molecular weight is crucial when working with molecules in biological systems like cellular membranes. It helps convert the mass of a substance into the number of moles, which is essential for comparing amounts of different molecular species. In our exercise, we used it to find the number of molecules within a given weight of the plasma membrane.

Molecular weight, expressed in grams per mole, allows us to know how much one mole of a given molecule weighs. The molecular weights provided were 50,000 g/mol for proteins and 750 g/mol for phospholipids. By applying these values in the formula for moles: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]we translated masses into moles. This translation not only aids in calculating ratios but also helps in other biochemical computations.

• A single mole of protein weighing 50,000 grams indicates a relatively larger and heavier molecule.
• A phospholipid's lower molecular weight signals smaller and lighter molecules.

Understanding these weights is vital, as it impacts how molecules are organized and interact at the cellular level.

Surface Area Coverage Estimation

Surface area coverage is an important metric for understanding cellular membrane composition and organization. To estimate how much of the membrane surface is covered by lipids, one would require specific knowledge about the size and arrangements of molecules involved.

Each phospholipid and protein molecule occupies space on the membrane. Measurements to consider may include the area occupied by a lipid or protein and the overall architecture, like bilayer formations or embedded proteins. Knowing the size of a single phospholipid molecule versus a protein molecule would allow us to estimate what fraction of the total membrane area is lipid-covered.

• Larger protein molecules may cover more or less area depending on how they are positioned in or on the membrane.
• Phospholipids usually form a bilayer, crucial for membrane integrity and function, and contribute to overall coverage.
• The ratio of lipid to protein molecules provides context but needs additional surface area data to complete the analysis.

Incorporating exact molecular sizes and arrangement patterns can enable a comprehensive coverage estimation, optimizing our understanding of biological membranes.