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 [math]\displaystyle{ t }[/math] (in hours) required for sedimentation of a fraction with a known sedimentation coefficient [math]\displaystyle{ s }[/math] (in svedbergs):

[math]\displaystyle{ t = \frac{k}{s} }[/math]

The value of the clearing factor depends on the maximum angular velocity [math]\displaystyle{ \omega }[/math] of a centrifuge (in rad/s) and the minimum and maximum radius [math]\displaystyle{ r }[/math] of the rotor:

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

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

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

Centrifuge manufacturers usually specify the minimum, maximum and average radius of a rotor, as well as the [math]\displaystyle{ k }[/math] factor of a centrifuge-rotor combination.

For runs with a rotational speed lower than the maximum rotor-speed, the [math]\displaystyle{ k }[/math] factor has to be adjusted:

[math]\displaystyle{ k_{\rm{adj}} = k \left( \frac{\mbox{maximum rotor-speed}}{\mbox{actual rotor-speed}} \right) }[/math]²

The K-factor is related to the sedimentation coefficient [math]\displaystyle{ S }[/math] by the formula:

[math]\displaystyle{ T = \frac{K}{S} }[/math]

Where [math]\displaystyle{ T }[/math] is the time to pellet a certain particle in hours. Since [math]\displaystyle{ S }[/math] is a constant for a certain particle, this relationship can be used to interconvert between different rotors.

[math]\displaystyle{ \frac{T_1}{K_1} = \frac{T_2}{K_2} }[/math]

Where [math]\displaystyle{ T_1 }[/math] is the time to pellet in one rotor, and [math]\displaystyle{ K_1 }[/math] is the K-factor of that rotor. [math]\displaystyle{ K_2 }[/math] is the K-factor of the other rotor, and [math]\displaystyle{ T_2 }[/math], 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