How many ribosomes are actively synthesizing proteins at any...

How many ribosomes are actively synthesizing proteins at any instant in an $E$. coli cell growing with a 45 -min doubling time? The birth size of $E$. coli is $1-\mu \mathrm{m}$ diameter and $2-\mu \mathrm{m}$ length. The water content is $75 \%$. About $60 \%$ of the dry material is protein, and the rate of amino acid addition per ribosome is 20 amino acids per second. The average molecular weight of free amino acids in $E$. coli is 126 .

Key Concepts

Doubling Time

Doubling time is a measure of how quickly a bacterial population grows, representing the time it takes for the number of cells to double. It is critical for understanding the overall growth dynamics, cellular metabolism, and the timing of biosynthetic processes, including protein synthesis. This parameter helps relate the rate of cell mass increase to the requirements for ribosome production and activity.

Protein Synthesis and Translation Rate

Protein synthesis in cells involves the sequential addition of amino acids to a growing polypeptide chain, a process governed by the translation rate of ribosomes. The translation rate provides a quantitative measure of how many amino acids a ribosome can incorporate per unit time, which is essential for estimating the number of ribosomes needed to meet the protein production requirements during rapid growth.

Ribosome Function and Activity

Ribosomes are the molecular machines responsible for translating mRNA into proteins. Their activity level, specifically the fraction that is actively engaged in protein synthesis at any given moment, is a key factor in determining the overall protein production capacity of the cell. In fast-growing cells, a large portion of the ribosomes must be active to sustain the high demand for protein synthesis.

Cellular Biomass Composition

The cellular biomass composition, particularly the proportion of water, proteins, and other dry matter components, is important for estimating the total protein content within a cell. Understanding this composition allows for calculations that relate cellular volume or size to the amount of protein that must be synthesized, thereby informing estimates on the number of actively translating ribosomes necessary to support growth.

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