Convert Mass into Volume » History » Revision 3
Revision 2 (Neil Voss, 02/05/2010 04:16 PM) → Revision 3/4 (Neil Voss, 02/05/2010 04:19 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 *''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;__ 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.__ ''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.__ ?? ''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.__ ?? ''i.e.'' a diameter of 122.7 Å Å??