Question

A purified pepsin was subjected to amino acid analysis. The amino acid present in the smallest amount was lysine, \(\mathrm{C}_{6} \mathrm{H}_{14} \mathrm{~N}_{2} \mathrm{O}_{2}\) and the amount of lysine was found to be \(0.431 \mathrm{~g}\) per \(100 \mathrm{~g}\) of protein. The minimum molecular mass of protein is: (a) \(34 \mathrm{u}\) (b) \(3400 \mathrm{u}\) (c) \(34,000 \mathrm{u}\) (d) \(3400,000 \mathrm{u}\)

Short answer

The minimum molecular mass of the protein is \(34,000\, \text{u}\), which corresponds to option (c).

Step-by-step solution

Determine the Molar Mass of Lysine

First, calculate the molar mass of lysine using its molecular formula \(\text{C}_6\text{H}_{14}\text{N}_2\text{O}_2\). Begin by adding the molar masses of its constituent elements: \(6\times 12.01\,\text{g/mol (C)} + 14\times 1.01\,\text{g/mol (H)} + 2\times 14.01\,\text{g/mol (N)} + 2\times 16.00\,\text{g/mol (O)}\). This calculation yields a total molar mass of lysine, \(146.19\, \text{g/mol}\).

Calculate the Moles of Lysine

Using the mass of lysine and its molar mass, calculate the number of moles of lysine. Given that the lysine mass is \(0.431\, \text{g}\), use the formula: \(\text{moles of lysine} = \frac{0.431 \, \text{g}}{146.19 \, \text{g/mol}}\). The calculation gives approximately \(0.00295\, \text{mol of lysine}\).

Relate to Protein Mass

Since lysine is the least abundant amino acid in the protein and there’s at least one mole of lysine per mole of protein, the moles of lysine hint at the minimum number of moles of protein. Given \(0.00295\, \text{mol of lysine}\) per \(100\, \text{g of protein}\), relate it as the minimum to be \(1\, \text{mol of protein}\).

Calculate Minimum Molecular Mass of Protein

To find the minimum molecular mass of the protein, calculate \(\frac{100 \, \text{g protein}}{0.00295 \, \text{mol protein}}\). This results in a molecular mass of protein of \(33,898.31\, \text{g/mol}\), which after rounding gives approximately \(34,000\, \text{u}\).

Choose the Correct Option

Based on the calculated molecular mass, compare against provided options. The closest match is (c) \(34,000\, \text{u}\).

Key concepts

Amino Acid Analysis

Amino acid analysis is a crucial process used to determine the composition and quantity of amino acids in a protein. This information is fundamental in understanding the protein's structure and function. Proteins are made up of long chains of amino acids, and each protein has a unique sequence and composition of amino acids.

In practice, amino acid analysis involves breaking down the protein into its individual amino acids and then quantifying them. This is typically done using techniques such as chromatography or mass spectrometry, which separate and measure the amino acids.

Knowing which amino acids are present, and in what amounts, can tell us much about the protein. It can also help identify defects or changes in protein that might be caused by diseases.

Lysine Composition

Lysine is one of the essential amino acids, meaning it must be obtained through the diet, as the human body cannot synthesize it. It plays a vital role in many biological processes, including protein synthesis, hormone production, and immune function.

In the context of amino acid analysis, lysine's composition within a protein can provide information about the protein's properties and stability. The lysine content can indicate how susceptible the protein is to modifications like glycation, where sugars attach to lysine residues and potentially alter the protein's function.

During the analysis, determining the amount of lysine becomes essential, especially when it is the least abundant amino acid, as it can affect the calculation of the minimum molecular mass of the protein. This is because the amount of lysine sets the baseline for the smallest possible protein size.

Minimum Molecular Mass

The minimum molecular mass of a protein is a calculation derived to ascertain the smallest possible size of the protein based on its amino acid composition. This is particularly useful when analyzing a protein's building blocks to determine its structure and function.

Calculating this involves understanding the mass of the amino acids present, especially the one that appears in the smallest quantity, as this sets a minimum threshold. In the given exercise, the presence of lysine in the smallest amount dictates the calculation based on its molar mass, leading to a complete protein mass calculation.

The step-by-step solution provided in the exercise shows how to compute this mass. By dividing the protein's known mass by the number of moles of lysine, we determine the minimum molecular mass, yielding insight into the minimal structural framework of the protein.

Protein Structure

Protein structure is often broken down into four levels: primary, secondary, tertiary, and quaternary. These levels describe the protein's complexity from its sequence of amino acids all the way to its 3D structure and functional complexes.

The primary structure refers to the amino acid sequence, which defines the protein's specific characteristics and biological activity. Within the context of this exercise, the primary structure is illustrated through the analysis of lysine and its impact on determining molecular mass.

The higher levels of structure involve folding and bonding interactions that bring about the protein's unique shape and functionality. Understanding the protein structure through amino acid analysis helps in numerous fields, including drug design, understanding disease mechanisms, and bioengineering.