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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 &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 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 &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.'' 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.'' 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.'' a diameter of 122.7 &Aring;?? &Aring;