Question

Refer to a typical Escherichia coli bacterium. This is a cylindrical cell about \(2 \mu\) m long and \(1 \mu\)m in diameter, weighing about \(2 \times 10^{-12}\)g and containing about \(80 \%\) water by volume. The cell is about \(15 \%\) protein by mass with \(90 \%\) of the protein in the cytoplasm. Assuming an average molecular mass of \(3 \times 10^{4}\) u, how many protein molecules are present in the cytoplasm?

Short answer

There are approximately \(6.022 \times 10^{6}\) protein molecules present in the cytoplasm of the bacterium.

Step-by-step solution

Calculate the mass of the bacterial cell

The mass of Escherichia coli cell is given as \(2 \times 10^{-12}\) g. It is a cylindrical cell about \(2 \mu\)m long and \(1 \mu\)m in diameter, weighing about \(2 \times 10^{-12}\) g and containing about \(80 \%\) water by volume. The mass becomes \(2 \times 10^{-12}\) g.

Determine the mass of protein

The cell is about \(15 \%\) protein by mass. Therefore, the mass of protein in the cell would be \(0.15 \times 2 \times 10^{-12}\) g = \(3 \times 10^{-13}\) g.

Calculate the number of protein molecules

We know that \(1\) mole of a substance contains \(6.022 \times 10^{23}\) entities (Avogadro's number). Also, given that the average molecular mass of the protein is \(3 \times 10^{4}\) u, which is equivalent to \(3 \times 10^{4}\) g/mol. The number of moles of protein = mass/molecular mass = \(3 \times 10^{-13}\) g / \(3 \times 10^{4}\) g/mol = \(1 \times 10^{-17}\) mol. So, the number of molecules = moles \times Avogadro's number = \(1 \times 10^{-17}\) mol \times \(6.022 \times 10^{23}\) /mol = \(6.022 \times 10^{6}\) protein molecules.

Key concepts

Mass and Size of Escherichia coli

Understanding the mass and size of a typical Escherichia coli bacterium is important for many microbiology studies. This rod-shaped bacteria is about (2 micrometers) long and (1 micrometer) in diameter. Despite its small size, the cell’s weight is approximately (2 × 10^-12 grams). It's fascinating to consider that such a microscopic organism has a complex structure and is capable of carrying out life processes.

The understanding of its size and weight is crucial not only for scientists studying bacterial behavior and infection patterns but also for students learning about microbiology. The measures give an insight into how life functions at a microscopic scale and the complexity of even the smallest forms of life.

Protein Content in Bacterial Cells

Proteins play a pivotal role in the life of a cell, carrying out a vast array of functions. In Escherichia coli, as in other bacteria, they comprise a significant portion of the cell's components. Approximately (15% of the bacterial cell’s mass) is protein, reflecting the important roles these molecules play, from structure to regulating biological processes.

Within the cell, a large concentration of these proteins, (90%), is found in the cytoplasm - the gel-like substance filling the cell. This concentration indicates that proteins are largely responsible for the cell's metabolic activities and general maintenance. For students, recognizing the protein content of bacterial cells not only illustrates their abundance but also offers insights into the biochemical makeup necessary for life.

Avogadro's Number and Molecular Mass

A fundamental concept in chemistry is Avogadro's number and its relation to molecular mass. Avogadro's number, roughly (6.022 × 10²³), is the number of units (such as atoms or molecules) in one mole of any substance. When it comes to quantifying substances at the molecular level, this number becomes essential.

The (average molecular mass) of a protein molecule, in this case of a protein in E. coli, is estimated to be about (3 × 10⁴ u), or unified atomic mass units. Expressing this mass in grams per mole allows us to use Avogadro's number to estimate the number of molecules in a given sample. By establishing the relationship between the mass in grams and the molecular mass in grams per mole, students can solve for the number of protein molecules in an E. coli cell, providing a direct connection between theoretical calculations and the physical realities within a cell.