Appion

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 &Aring;<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 &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 &pi; 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 &pi; 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