Sanford-Wang parameterisation

In centrifugation the clearing factor or k factor represents the relative pelleting efficiency of a given centrifuge rotor at maximum rotation speed. It can be used to estimate the time $t$ (in hours) required for sedimentation of a fraction with a known sedimentation coefficient $s$ (in svedbergs):

$t=\frac{k}{s}$

The value of the clearing factor depends on the maximum angular velocity $\omega$ of a centrifuge (in rad/s) and the minimum and maximum radius $r$ of the rotor:

$k=\frac{\ln (r_{\mathrm{m}\mathrm{a}\mathrm{x}}/r_{\mathrm{m}\mathrm{i}\mathrm{n}})}{{\omega }^2}\times \frac{10^{-13}}{3600}$

As the rotational speed of a centrifuge is usually specified in RPM, the following formula is often used for convenience:

$k=\frac{2.53\cdot 10^5\times \ln (r_{\mathrm{m}\mathrm{a}\mathrm{x}}/r_{\mathrm{m}\mathrm{i}\mathrm{n}})}{(\mathrm{R}\mathrm{P}\mathrm{M}/\mathrm{1}\mathrm{0}\mathrm{0}\mathrm{0}{\mathrm{)}}^{\mathrm{2}}}$

Centrifuge manufacturers usually specify the minimum, maximum and average radius of a rotor, as well as the $k$ factor of a centrifuge-rotor combination.

For runs with a rotational speed lower than the maximum rotor-speed, the $k$ factor has to be adjusted:

$k_{\mathrm{a}\mathrm{d}\mathrm{j}}=k\left(\frac{\text{maximum rotor-speed}}{\text{actual rotor-speed}}\right)$²

The K-factor is related to the sedimentation coefficient $S$ by the formula:

$T=\frac{K}{S}$

Where $T$ is the time to pellet a certain particle in hours. Since $S$ is a constant for a certain particle, this relationship can be used to interconvert between different rotors.

$\frac{T_1}{K_1}=\frac{T_2}{K_2}$

Where $T_1$ is the time to pellet in one rotor, and $K_1$ is the K-factor of that rotor. $K_2$ is the K-factor of the other rotor, and $T_2$, the time to pellet in the other rotor, can be calculated. In this manner, one does not need access to the exact rotor cited in a protocol, as long as the K-factor can be calculated. Many online calculators are available to perform the calculations for common rotors.

References

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External links

• Beckman Coulter lab resources and manuals
• Appendix F of the Cell Biology Laboratory Manual