# 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 (rmax), and minimum radius (rmin)—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

 Rotor Type Type 70 Ti Type 70.1Ti Maximum Speed 70,000 rpm 70,000 rpm Maximum radius (rmax) 91.9 mm 82 mm Minimum radius (rmin) 39.5 mm 40.5 mm Maximum g-force 504,000 x g 450,000 x g Total pathlength 52.4 mm 41.5 mm k-factor 44 36

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.

 Rotor J-LITE JLA-8.1000 J-LITE JLA-9.1000 Fiberlite™ F9-6 x 1,000 LEX Fiberlite F8-6 x 1,000y Fiberlite F5-10 x 1,000 LEX Fiberlite F6-6 x 1,000y Type Fixed-Angle Fixed-Angle Fixed-Angle Fixed-Angle Fixed-Angle Fixed-Angle Maximum volume (mL) 6x1,000 4x1,000 6x1,000 6x1,000 10x1,000 6x1,000 Maximum speed (rpm) 8,000 9,000 9,000 8,500 5,500 6,000 Minimum radius (mm) 119 82 65 54 124 54 Maximum radius (mm) 222.8 185 194 196 275 196 Maximum g-force 15,970 x g 16,800 x g 17,568 x g 15,900 x g 9,333 x g 7,900 x g Total pathlength (mm) 103.8 103 129 142 151 142 k-factor with largest volume at max speed 2,482 2,540 3,415 5,096 6,662 9,060

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

 Rotor Max Speed (rpm) Max RCF (g-force) Rotor Places x Volume (mL) k-Factor with Largest Volume Tube at Max Speed k-Factor with g-Max Tube Volume of g-Max Tube (mL) Fixed-Angle Rotors Type 100 Ti 100,000 802,400 8x6.8 15 7 2 Type 90 Ti 90,000 694,000 8x13.5 25 11 4.2 Type 70.1 Ti 70,000 450,000 12x13.5 36 17 4.2 Type 70 Ti 70,000 504,000 8x39 44 24 15 Type 50.2 Ti 50,000 302,000 12x39 62 39 15 Type 45 Ti 45,000 235,000 6x94 133 — — Type 50.4 Ti 50,000 270,000 44x6.5 39 15 2 Type 42.2 42,000 223,000 72x0.230 9 — — Type 25 25,000 92,500 100x1 62 — — Type 19 19,000 53,900 6x250 951 — — Near-Vertical & Vertical Tube Rotors NVT 100 100,000 750,000 13x51 8 6 2 NVT 90 90,000 645,000 8x5.1 10 7 2 NVT 65.2 65,000 416,000 16x5.1 15 7 2 NVT 65 65,000 402,000 8x13.5 21 8 6.3 VTi 90 90,000 645,000 8x5.1 6 6 3.5 VTi 65.1 65,000 402,000 8x13.5 13 13 6.3 VTi 50 50,000 242,000 8x39 36 36 15 VTi 65.2 65,000 416,000 16x5.1 10 10 2 Swinging Bucket Rotors SW 60 Ti 60,000 485,000 6x4 45 24 1.5 SW 55 Ti 55,000 368,000 6x5 48 29 2 SW 41 Ti 41,000 288,000 6x13.2 124 27 3.5 SW 40 Ti 40,000 285,000 6x14 137 35 3.5 SW 32 Ti 32,000 175,000 6x38.5 204 74 8.4 SW 32.1 Ti 32,000 187,000 6x17 229 56 4.5 SW 28 28,000 141,000 6x38.5 246 87 15 SW 28.1 28,000 150,000 6x17 276 67 4.2

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

 Rotor Max Speed (rpm) Max RCF (g-force) Rotor Places x Volume (mL) k-Factor with Largest Volume Tube at Max Speed k-Factor with g-Max Tube Volume of g-Max Tube (mL) Fixed-Angle Rotors TLA-120.1 120,000 627,000 14x0.5 8 — — TLA-120.2 120,000 627,000 10x2.0 16 14 1.5 TLA-110 110,000 657,000 8x5.1 13 5 2.0 TLA-100 100,000 436,000 20x0.2 7 — — TLA-100.3 100,000 541,000 6x3.5 14 11 2.0 TLA-55 55,000 186,000 12x1.5 66 — — MLA-150 150,000 1,003,000 8x2.0 10.4 6.2 1.5 MLA-130 130,000 1,019,000 10x2.0 8.7 7 1.5 MLA-80 80,000 444,000 8x8.0 29 18 4.2 MLA-55 55,000 287,000 8x13.5 53 28 4.2 MLA-50 50,000 233,000 6x32.4 92 50 15 Near-Vertical & Vertical Tube Rotors TLN-120 120,000 585,000 8x1.2 7 — — TLN-100 100,000 450,000 8x3.9 14 — — MLN-80 80,000 389,000 8x8.0 20 16 4.1 Swinging Bucket Rotors TLS-55 55,000 259,000 4x2.2 50 37 1.5 MLS-50 50,000 268,000 4x5.0 71 29 2.0

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

JS-24.15
 Rotor Max Speed (rpm) Max RCF (g-force) Rotor Places x Volume (mL) k-Factor with Largest Volume Tube at Max Speed Fixed-Angle Rotors JA-30.50 Ti 30,000 108,860 8x50 280 JA-25.50 25,000 75,600 8x50 418 JA-25.15 25,000 Outer Row: 74,200 Inner Row: 60,200 24x15 Outer Row: 265 Inner Row: 380 JA-21 21,000 50,400 18x10 470 JA-20.1 20,000 Outer Row: 51,500 Inner Row: 43,900 32x15 Outer Row: 371 Inner Row: 465 JA-20 20,000 48,400 8x50 769 JA-18.1 18,000 42,100 24x1.8 156 JA-18 18,000 47,900 10x100 566 JA-17 17,000 39,800 14x50 690 J-LITE JLA-16.250 16,000 38,400 6x250 1,090 JA-14.50 14,000 35,000 16x50 787 JA-14 14,000 30,100 6x250 1,764 JA-12 12,000 23,200 12x50 1,244 J-LITE JLA-10.500 10,000 18,600 6x500 2,850 JA-10 10,000 17,700 6x500 3,610 J-LITE JLA-9.1000 9,000 16,800 4x1,000 2,544 J-LITE JLA-8.1000 8,000 15,970 6x1,000 2,482 Swinging Bucket Rotors 24,000 110,500 6x15 376 JS-24.38 24,000 103,900 6x38.5 334 JS-13.1 13,000 26,500 6x50 1,841 JS-7.5 7,500 10,400 4x250 5,287 JS-5.9 5,900 6,570 — — JS-5.3 5,300 Conical Bottles: 6,870 Deep-Well Plates: 6,130 4x500 Conical Bottles: 7,728 Deep-Well Plates: 1,536 JS-5.0 5,000 7,480 4x2,250 9,171 JS-4.3 4,300 4,220 4x750 11,800 JS-4.2 4,200 5,020 6x1,000 11,500 JS-4.0 4,000 4,050 4x1,000 15,300

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

CENT-66APP07.14-B