Clearing factor

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:

\[k = \frac{\ln(r_{\rm{max}} / r_{\rm{min}})}{\omega^2} \times \frac{10^{-13}}{3600}\]

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

\[k = \frac{2.53 \cdot 10^5 \times \ln(r_{\rm{max}} / r_{\rm{min}})}{(\rm{RPM}/1000)^2}\]

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:

\[k_{\rm{adj}} = k \left( \frac{\mbox{maximum rotor-speed}}{\mbox{actual rotor-speed}} \right)\]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.

External links

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