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 ų/Da = NA×10−24 = 0.6022 ml/g

We can convert the density into cubic Ångstroms per Dalton:

• Protein density is 1.209 ų/Da
• RNA density is 0.958 ų/Da

Converting into a diameter

• given macromolecule mass, m in Daltons, macromolecule protein mass, m_p in Daltons, and macromolecule RNA mass, m_r in Daltons;

*Case 1, Particle is spherical:

• 4/3 π r^3 = m_p * 1.209 + m_r * 0.958

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

• 2/3 π r^3 = m_p * 1.209 + m_r * 0.958

Examples === 400 kDa protein ===

• Mass:
  • m_p = 400,000
  • m_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