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Convert Mass into Volume » History » Revision 2

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Neil Voss, 02/05/2010 04:16 PM


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</sup>/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</sup>/Da
  • RNA density is 0.958 Å<sup>3</sup>/Da
Converting into a diameter

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

*Case 1, Particle is spherical:
4/3 π r^3 = m<sub>p</sub> * 1.209 + m<sub>r</sub> * 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</sub> * 1.209 + m<sub>r</sub> * 0.958

Examples === 400 kDa protein ===
  • Mass:
    • m<sub>p</sub> = 400,000
    • m<sub>r</sub> = 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??

Updated by Neil Voss over 14 years ago · 2 revisions