Size and Shape of Protein Molecules at the Nanometer Level Determined by Sedimentation, Gel Filtration, and Electron Microscopy

An important part of characterizing any protein molecule is to determine its size and shape. Sedimentation and gel filtration are hydrodynamic techniques that can be used for this medium resolution structural analysis. This review collects a number of simple calculations that are useful for thinking about protein structure at the nanometer level. Readers are reminded that the Perrin equation is generally not a valid approach to determine the shape of proteins. Instead, a simple guideline is presented, based on the measured sedimentation coefficient and a calculated maximum S , to estimate if a protein is globular or elongated. It is recalled that a gel filtration column fractionates proteins on the basis of their Stokes radius, not molecular weight. The molecular weight can be determined by combining gradient sedimentation and gel filtration, techniques available in most biochemistry laboratories, as originally proposed by Siegel and Monte. Finally, rotary shadowing and negative stain electron microscopy are powerful techniques for resolving the size and shape of single protein molecules and complexes at the nanometer level. A combination of hydrodynamics and electron microscopy is especially powerful.

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Most proteins fold into globular domains. Protein folding is driven largely by the hydrophobic effect, which seeks to minimize contact of the polypeptide with solvent. Most proteins fold into globular domains, which have a minimal surface area. Peptides from 10 to 30 kDa typically fold into a single domain. Peptides larger than 50 kDa typically form two or more domains that are independently folded. However, some proteins are highly elongated, either as a string of small globular domains or stabilized by specialized structures such as coiled coils or the collagen triple helix. The ultimate structural understanding of a protein comes from an atomic-level structure obtained by X-ray crystallography or nuclear magnetic resonance. However, structural information at the nanometer level is frequently invaluable. Hydrodynamics, in particular sedimentation and gel filtration, can provide this structural information, and it becomes even more powerful when combined with electron microscopy (EM).

One guiding principle enormously simplifies the analysis of protein structure. The interior of protein subunits and domains consists of closely packed atoms (1 ). There are no substantial holes and almost no water molecules in the protein interior. As a consequence of this, proteins are rigid structures, with a Young’s modulus similar to that of Plexiglas (2 ). Engineers sometimes categorize biology as the science of “soft wet materials”. This is true of some hydrated gels, but proteins are better thought of as hard dry plastic. This is obviously important for all of biology, to have a rigid material with which to construct the machinery of life. A second consequence of the close packed interior of proteins is that all proteins have approximately the same density, about 1.37 g/cm³ . For most of the following, we will use the partial specific volume, v ₂ , which is the reciprocal of the density. v ₂ varies from 0.70 to 0.76 for different proteins, and there is a literature on calculating or determining the value experimentally. For the present discussion, we will ignore these variations and assume the average v ₂= 0.73 cm³ /g.

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The inverse relationship is also frequently useful: M (Da) = 825 V (nm³ ).