Convert Mass into Volume » History » Revision 2
Revision 1 (Neil Voss, 02/05/2010 04:04 PM) → Revision 2/4 (Neil Voss, 02/05/2010 04:16 PM)
h1. 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 :1 Å<sup>3</sup>/Da = NA×10−24 = 0.6022 ml/g?? 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 :4/3 π r^3 = m<sub>p</sub> * 1.209 + m<sub>r</sub> * 0.958?? 0.958 *Case 2, Particle is flattened like an M&M candy, ''i.e.'' an oblate spheroid: ??2/3 :2/3 π r^3 = m<sub>p</sub> * 1.209 + m<sub>r</sub> * 0.958?? 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 :4/3 π r^3 = 400,000 * 1.209?? 1.209 ??r :r = (400,000 * 1.209 * 3 / 4 / π)^(1/3) = 48.7 Å?? Å ?? : ''i.e.'' a diameter of 97.4 Å?? Å *Case 2, Particle is flattened: ??2/3 :2/3 π r^3 = 400,000 * 1.209?? 1.209 ??r :r = (400,000 * 1.209 * 3 / 2 / π)^(1/3) = 61.3 Å?? Å ?? : ''i.e.'' a diameter of 122.7 Å?? Å