Using k-Factor to Compare Rotor Efficiency

Most researchers refer to the maximum speed of a rotor to compare efficiency. This can be misleading, however, since other factors such as the geometry of the tube or temperature contribute to rotor performance and must be considered before a valid comparison between similar rotors can be made. Some rotors are more efficient at slower speeds than a comparable rotor at higher speeds, simply because of the influence of these additional factors. So, we recommend using the term k-factor, rather than maximum speed, to compare centrifugation labware.

The k-factor is a common parameter that describes the efficiency of a centrifuge-rotor system, although temperature is still overlooked. Temperature complicates the determination and cannot be used in a simple formula; however, it can be managed in programs such as Beckman Coulter’s eXPert software that factors in the temperature and corrects for buffer viscosities. k-factor, however, is still an excellent determination for rotor efficiency, as it includes all parameters to replicate a centrifugation step and clearly defines the proficiency of a centrifugerotor system.

The Determinants of k-Factor

The most important contributors to rotor efficiency are the maximum speed, maximum radius (r_max), and minimum radius (r_min)—all of which contribute to the maximum g-force generated by the rotor. Firstly, the greater the minimum radius, the greater the centrifugal force at the top of the tube, and the faster the separation will proceed. Furthermore, the centrifugal force at the rmin defines the minimum size of a particle to start sedimentation. Another factor that has a direct bearing on rotor efficiency is the total pathlength of the rotor, or the difference between maximum and minimum radius. Shorter pathlengths mean particles have less distance to travel before pelleting against the tube wall. Pathlengths in similar rotors are a function of the diameter of the sample tube and the angle at which the tube is held. A more sharply angled tube generally results in a shorter pathlength. A simple measure of overall rotor efficiency that takes into consideration these variables is the k-factor, where:

A lower k-factor corresponds to a more efficient rotor.

Comparative Efficiencies of Two 70,000 rpm Rotors

Applying the aforementioned efficiency factors to runs of the Beckman Coulter Type 70.1 Ti and Type 70 Ti rotors yield interesting results. The following example demonstrates how the Type 70.1 Ti at 450,000 x g will actually pellet material faster than a Type 70 Ti at a higher RCF (504,000 x g) when both are run at the same rotations per minute (70,000 rpm). As you can see in Table 1, the geometry of the tube cavity for the Type 70.1 Ti serves to decrease the maximum radius of the rotor (leading to a lower g-force) but also decreases the pathlength of the particles within the sample tube. The net effect of this reduced pathlength is a more favorable k-factor for the Type 70.1 Ti, resulting in more than 18% faster pelleting time than in the Type 70 Ti.

Table 1. Rotor Specifications

Bovine Serum Albumin (BSA) is a common protein in research utilized for a multitude of purposes with a sedimentation coefficient (s) of 4.4s. Using the previous k-factors calculated in Table 1, for example, if an experimenter desired to pellet BSA using a Type 70 Ti rotor, the pelleting time can be calculated as such, where t is the run time in hours required to pellet particles of known sedimentation coefficient (in Svedberg units, s):

This simple calculation helps researchers save valuable time, and spin for the most efficient duration. In comparing the run time for the Type 70.1 Ti with BSA by substituting a k-factor of 36 generates a time of 8 hours, 11 minutes, demonstrating that a rotor with a smaller maximum g-force can actually be more efficient.

Relating Run Time Between Labware

Two popular, high-performance rotors in the Beckman Coulter, Inc. line are the SW 28 and the SW 32 Ti. To compare run times between two rotors in order to duplicate a particular centrifugation step, a researcher only needs to know the k-factor of each rotor and the duration of the run from a previous method. Use the following equation, where k1 and k2 are the k-factors of the SW 32 Ti and SW 28 respectively, t2 is the duration of a previous protocol’s run, and t1 is the unknown spin time for the SW 32 Ti rotor:

This is another simple calculation which facilitates researchers in comparing methods between 2 different centrifugerotor systems. This equation helps to equally sediment particles and compares efficiency among labware.

As previously mentioned, the k-factor of a rotor is determinant upon the pathlength (rmax/rmin) of the standard tube for the specified rotor. If a researcher is restricted to a specific rotor geometry and maximum g-force, improvements to k-factor can still be achieved by decreasing pathlength. One such example is the use of Beckman Coulter, Inc. g-Max tubes. This innovative system uses patented Beckman Coulter Quick-Seal bell-top polyallomer tubes and floating spacers. Unlike conventional sleevetype adapters, the g-Max spacers “float” on top of the tube and the sample is kept at the maximum radius of the tube cavity—shortening the pathlength of the standard tube for the specified rotor—allowing you to run smaller volumes of samples without a reduction in g-force. In rotors where g-Max tubes correspond to a shorter pathlength and smaller k-factor, the run duration can be reduced, saving critical time in researchers’ lives. g-Max tubes are compatible with most Beckman Coulter ultracentrifuge rotors.

In Figure 1, the g-Max technology exhibits the large amounts of time researchers can save by utilizing different labware. In the Type 90 Ti rotor, the k-factor of a 4.2 mL g-Max tube is 11 compared to a 13.5 mL tube with a k-factor of 25, both spun at 90,000 rpm. Figure 1 illustrates an example where g-Max technology results in a 56% savings in time between the two tubes. In many applications,

Figure 1.Comparative efficiency of g-Max technology.

an overnight spin of 18 hours is required. However, with the g-Max tube, equivalent separations are achieved in less than 8 hours, better fitting within a typical workday and generating a more convenient workflow.

k-Factors and Large-Scale Vaccine Production

k-factors affect the pelleting time of all types of centrifuges, not just ultracentrifuges as previously discussed. The following example will illuminate how k-factor affects rotor efficiency in high-performance centrifuges. Large-scale production of vaccines is critical to the human race in order to combat widespread plagues and eradicate illnesses throughout the world. In many cases, cells are harvested by high-capacity centrifugation at speeds of around 5,000 x g. Traditionally, this application has been performed in swinging bucket rotors; however, highthroughput is most critical to researchers in the field to increase yield and shorten the time to market. Table 2 demonstrates that Beckman Coulter, Inc. rotors, J-LITE JLA-8.1000 and J-LITE JLA-9.1000, are well-designed and minimize the k-factor while processing large volumes in a single spin. This saves valuable lab time, rotor wear, and electricity costs, since low k-factors correspond to high-efficiency. Furthermore, during vaccine production, after the initial cell pelleting step, purification of the pathogenic virus antigens requires speeds in excess of 15,000 x g—a capability ubiquitous in both of the Beckman Coulter 1-liter high-capacity rotors, adding functionality to already efficient rotors. Beckman Coulter provides manufacturers the ability to improve process performance, reduce costs, and shorten time to market.

Table 2. Comparison of High-Capacity Fixed Angle 1-Liter Rotors.

Table 3. Preparative Ultracentrifuge Rotors and Corresponding k-Factors.

Table 4. Micro-Ultracentrifuge Rotors and Corresponding k-Factors.

Table 5. High-Performance Rotors and Corresponding k-Factors.

Please see rotor manuals for a complete listing of available tube sizes and for any additional information. For additional rotor calculation information, visit www.beckman.com

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