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## Partial-specific volumes

Since sedimentation experiments take place in solvent, the buoyancy of the particles is an important factor, and therefore we need to know their volume.  As long as we are in dilute buffered solutions, two-component theory applies and we can describe the buoyant molar mass as Mb = M(1-vr), with M the particle mass, v it's partial-specific volume, and r the density of the solvent.

(If you are dealing with a three-component system in the presence of preferential solvation, you could describe the buoyancy as Mb = Mdr/dc with the density increment dr/dc, or you could use an 'effective partial-specific volume' for the solvated particle under the given solvent conditions, Mb = M(1-F'r)).

In SedPHaT, there are three issues important to know with regard to the partial-specific volume:

1)  Each experiment has a local partial-specific volume, to be entered in the Experimental Parameters box.  This is valid only for the particular experiment, referring to the parameter v or F' for the solvent composition and temperature of this particular experiment.  This may be different from the global partial-specific volume, which refers to the conditions of water at 20C, and is entered in the options menu.  Ordinarily, for proteins in dilute buffered salt solution, this distinction is usually not critical, because the temperature dependence of the partial-specific volume is relatively small.

Obviously, if all experiments in the global analysis are performed at the same temperature and buffer composition, this is not be an issue.  However, this may not always be the case. In order to permit global analysis of data obtained at different solvent conditions (or temperature), this distinction is made.

In order to avoid inadvertent errors in the analysis of data from using wrong global v20,w values, this parameter is stored along with the other local parameters in the experiment.  After loading an experiment, this stored v20,w value is proposed as a value for the global parameter. 2)  If there are several experiments at different density, the partial-specific volume can be treated as a fitting parameter, but only under the assumption that the v value is the same for all experiments (fit vbar20 = vbar(T)). 3) For studies of heterogeneous interactions where we have two protein components A and B, there is a problem when using only one v-value.  Obviously, the partial-specific volume of the two proteins in general are different.

In the future, it is planned to incorporate into SedPHaT two different partial-specific volumes, one for each component.  In the meantime, however, you have to resort to the mathematical equivalent solution of using apparent molar mass values for one component. This is how this works:

Set all the partial-specific volume values to that of component A (call it vA).  The buoyant molar mass values MAb will then be, as usual, MAb = MA(1-vAr).  Similarly, the buoyant molar mass of component B will be MBb = MB(1-vBr).  We can now calculate the apparent molar mass value MB* which would give the correct MBb value if we use the partial-specific volume of component A: MBb =  MB*(1-vAr).  Since the measured quantities are the buoyant molar mass values, it doesn't matter if we use MB* as molar mass value with a partial-specific volume vA, or if we use the real molar mass MB with the real partial-specific volume of component B, vB.  Therefore, we can simply use instead of MB the apparent molar mass value MB* = MB(1-vBr)/(1-vAr).

Correcting the molar mass of B with the factor (1-vBr)/(1-vAr) may look strange and appear incorrect, since you may know the molar mass precisely, but it is entirely correct and mathematically equivalent to using a second partial-specific volume vB

Hopefully, future implementations will eliminate this inconvenience. 