Convert Mass into Volume

This page will help you convert the mass of a macromolecule into a diameter in a micrograph.

Denisities

  • Protein density is 0.728 ml/g

    • Y. Harpaz, M. Gerstein and C. Chothia, "Volume changes on protein folding", Structure 2 (1994), pp. 641--649.

  • RNA density is 0.577 ml/g

    • N.R. Voss and M. Gerstein, "Calculation of Standard Atomic Volumes for RNA and Comparison with Proteins: RNA is Packed More Tightly", JMB v346#2 (2005), pp. 477-492.

From the relation:

  • 1 Å<sup>3/Da = NA×10−24 = 0.6022 ml/g

We can convert the density into cubic Ångstroms per Dalton:

  • Protein density is 1.209 Å<sup>3/Da
  • RNA density is 0.958 Å<sup>3/Da

Converting into a diameter

  • given macromolecule mass, m in Daltons, macromolecule protein mass, m<sub>p in Daltons, and macromolecule RNA mass, m<sub>r in Daltons;

*Case 1, Particle is spherical:

  • 4/3 π r^3 = m<sub>p * 1.209 + m<sub>r * 0.958

Case 2, Particle is flattened like an M&M candy, i.e.* an oblate spheroid:

  • 2/3 π r^3 = m<sub>p * 1.209 + m<sub>r * 0.958

Examples

= 400 kDa protein =

  • Mass:
    • m<sub>p = 400,000
    • m<sub>r = 0

*Case 1, Particle is spherical:

4/3 π r^3 = 400,000 * 1.209

r = (400,000 * 1.209 * 3 / 4 / π)^(1/3) = 48.7 Å

i.e. a diameter of 97.4 Å

*Case 2, Particle is flattened:

2/3 π r^3 = 400,000 * 1.209

r = (400,000 * 1.209 * 3 / 2 / π)^(1/3) = 61.3 Å

i.e. a diameter of 122.7 Å