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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 &Aring;<sup>3</sup>/Da = NA×10−24 = 0.6022 ml/g ml/g?? 

 We can convert the density into cubic &Aring;ngstroms per Dalton: 
 * Protein density is 1.209 &Aring;<sup>3</sup>/Da 
 * RNA density is 0.958 &Aring;<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 &pi; 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 &pi; 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 &pi; r^3 = 400,000 * 1.209 1.209?? 
 ** r ??r =    (400,000 * 1.209 * 3 / 4 / &pi;)^(1/3) = 48.7 &Aring; &Aring;?? 
 ** __i.e.__ ?? ''i.e.'' a diameter of 97.4 &Aring; &Aring;?? 

 *Case 2, Particle is flattened: 
 ** 2/3 ??2/3 &pi; r^3 = 400,000 * 1.209 1.209?? 
 ** r ??r =    (400,000 * 1.209 * 3 / 2 / &pi;)^(1/3) = 61.3 &Aring; &Aring;?? 
 ** __i.e.__ ?? ''i.e.'' a diameter of 122.7 &Aring; &Aring;??