It is often stated that proteins are quite large compared to...

It is often stated that proteins are quite large compared to the molecules they bind. However, what constitutes a large number depends on your point of view. Calculate the ratio of the volume of a hemoglobin molecule $(65 \mathrm{kD})$ to that of the four $\mathrm{O}_{2}$ molecules that it binds and the ratio of the volume of a typical office $(4 \times 4 \times 3 \mathrm{m})$ to that of the typical (70-kg) office worker that occupies it. Assume that the molecular volumes of hemoglobin and $\mathrm{O}_{2}$ are in equal proportions to their molecular masses and that the office worker has a density of $1.0 \mathrm{g} / \mathrm{cm}^{3}$. Compare these ratios. Is this the result you expected?

Key Concepts

Dimensional Analysis and Scaling

Dimensional analysis is a method used to understand how different physical quantities scale with one another by comparing their dimensions. In the context of comparing molecular interactions and macroscopic phenomena, it helps to normalize differences in units and scale, allowing for meaningful comparisons between objects that exist over many orders of magnitude in size.

Volume Ratio Comparisons

Volume ratio comparisons involve taking the computed or estimated volumes of different entities and forming a ratio to evaluate their relative sizes. This technique is useful in many fields, including biochemistry and architecture, to understand how a smaller object (like a molecule or a person) relates in size to a larger structure (such as a protein complex or a building) and can reveal non?intuitive insights about the relative scales involved.

Volume Calculations Using Density

Density is defined as mass per unit volume and is used to convert mass to volume, especially in macroscopic systems. For example, by assuming a known density for a human body, one can calculate the volume occupied by that body from its mass. This principle is crucial when comparing the space occupied by objects on very different scales, like proteins versus office spaces.

Molecular Mass?Volume Proportionality

This concept assumes that for objects with similar densities, their volumes are directly proportional to their masses. In molecular systems, where molecules such as proteins and small gas molecules are treated as having comparable densities, the mass can be used as a proxy for volume. This simplifies the estimation of molecular volumes when comparing entities that differ significantly in mass.

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