E. coli can be induced to make about 10,000 copies of the...

E. coli can be induced to make about 10,000 copies of the lactose transporter $\left(M_{\mathrm{r}} 31,000\right)$ per cell. Assume that $E .$ coli is a cylinder $1 \mu \mathrm{m}$ in diameter and $2 \mu \mathrm{m}$ long. What fraction of the plasma membrane surface is occupied by the lactose transporter molecules? Explain how you arrived at this conclusion.

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Key Concepts

Occupancy Fraction Estimation

This concept is about calculating the fraction of the membrane area that is occupied by proteins. It involves taking the total area occupied by all protein molecules (derived from the number of proteins multiplied by the area per protein) and dividing it by the total cell membrane surface area. This ratio reflects the density of proteins relative to the available membrane space.

Cell Geometry and Surface Area Calculation

This concept involves using geometric principles to calculate the total surface area of a cell, particularly when the cell is approximated by a simple shape such as a cylinder. Understanding how to compute the lateral and end surface areas of a cylinder allows one to determine the total available plasma membrane area that proteins may occupy.

Membrane Protein Footprint Estimation

This concept deals with estimating the area that a single membrane protein occupies when embedded in the plasma membrane. It requires knowledge of the protein's structure and size in order to approximate its cross?sectional area. This estimation is crucial for determining the extent to which proteins can cover or be dense within the membrane.

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