Size and shape of protein molecules at the nanometer level determined by sedimentation, gel filtration, and electron microscopy

Abstract

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.

Figure 1

Glycerol gradient sedimentation analysis of SMC protein from B. subtilis (BsSMC; upper panel) and sedimentation standards catalase and bovine serum albumin (lower panel). A 200-μl sample was layered on a 5.0-ml gradient of 15–40% glycerol in 0.2 M ammonium bicarbonate and centrifuged in a Beckman SW55.1 swinging bucket rotor, 16 h, 38,000 rpm, 20°C. Twelve fractions of 400 μl each were collected from a hole in the bottom of the tube and each fraction was run on SDS-PAGE. Lane SM shows the starting material, and fraction 1 is the bottom of the gradient. The bottom panel shows that the 11.3-S catalase eluted precisely in fraction 4, while the 4.6-S BSA eluted mostly in fraction 8, with some in fraction 9. We estimated the BSA to be centered on fraction 8.2. Experiments with additional standard proteins have demonstrated that the 15–40% glycerol gradients are linear over the range 3–20 S, so a linear interpolation is used to determine S of the unknown protein. BsSMC is in fractions 7 and 8, estimated more precisely at fraction 7.3. Extrapolating from the standards, we determine a sedimentation coefficient of 6.0 S for BsSMC. Other experiments gave an average value of 6.3 S for BsSMC [19].

Figure 2

Each bead models a 10-kDa domain, with an assumed sedimentation coefficient of 1.42 S. The radius of the bead is 1.67 nm, using R_min = 1.42 nm, and adding 0.25 nm for a shell of water. The beads are an approximation to FN-III or Ig domains, which are ~1.7 × 2.8 × 3.5 nm. The sedimentation coefficients of multibead structures were calculated by the formula of Kirkwood/Bloomfield.

Figure 3

Determination of R_s of BsSMC by gel filtration. The column was calibrated by running standard proteins BSA, catalase, and thyroglobulin over the column, then BsSMC. BsSMC eluted in fraction 14.2, which corresponds to an R_s of 10 nm on the extrapolated curve. In repeated experiments, the average R_s was 10.3 nm [19].

Figure 4

Rotary shadowing EM of three highly elongated protein molecules: the SMC protein from B. subtilis [19], fibrinogen [20], and the hexabrachion protein, tenascin [21].

Figure 5

Hydrodynamic analysis of the DASH/Dam1 complex. Gel filtration is shown in a and sucrose gradient sedimentation in b. Independent calibration curves using standard proteins are shown in black and green. Dark and light blue show Spc34p in yeast cytoplasmic extract and in the purified recombinant protein. Red and purple show Hsk3p. The proteins were identified and quantitated by Western blot of the fractions, shown in c. The four protein bands eluted together at 1/D = 0.35 × 10⁷, corresponding to R_s = 7.6 nm, and at 7.4 S. Reproduced from Miranda et al. [24] with permission of the authors.

Figure 6

EM of DASH/Dam1. a Rotary shadowing shows particles roughly 13 nm in size, with irregular shape. b State-of-the-art negative stain coupled with single particle averaging shows a complex internal structure of the elongated particles. The scale bar indicates 100 nm for the unprocessed images. The averaged images on the right show a monomer, dimer, and trimer. These panels are 14 nm wide. The dimer was the predominant species. Left panel (rotary shadowing) reprinted with permission of Miranda et al. [24]. Right panels (negative stain) reprinted with permission of Wang et al. [26].