Researchers often compare efficiency by referring to the highest rotor speed, but this can be misleading because other factors such as temperature or geometry of the tube contribute to the performance of the rotor and should be factored if a valid comparison between similar rotors is going to be made.
Simply owing to the effect of these other factors, certain rotors are more efficient at slower speeds than a similar rotor at higher speeds. As a result, the term kfactor can be used instead of maximum speed, to compare centrifugation labware.
The kfactor is a common parameter describing the efficiency of a centrifugerotor system, but temperature is still overlooked. The determination of kFactor is complicated by temperature, which cannot be applied in a basic formula.
However, it can be managed in programs such as the eXPert software supplied by Beckman Coulter which factors in the temperature and corrects for buffer viscosities.
However, kfactor has all the parameters to replicate a centrifugation step and distinctly defines the ability of a centrifugerotor system, making it an excellent determination for rotor efficiency.
The Determinants of kFactor
The maximum speed, minimum radius (r_{min}), and maximum radius (r_{max}) are the most essential factors contributing to rotor efficiency, all of which contribute to the maximum gforce produced by the rotor.
First, the greater the minimum radius, the greater the centrifugal force at the top of the tube and the faster separation will proceed. In addition, the centrifugal force at the r_{min} defines a particle’s minimum size for starting sedimentation.
Another factor that directly contributes to rotor efficiency is the total pathlength of the rotor or the difference between minimum and maximum radius.
Shorter pathlengths mean particles do not have as far to travel prior to pelleting against the wall of the tube. Pathlengths in comparable rotors are a function of the sample tube diameter and the angle at which the tube is held.
A shorter pathlength generally arises from a more sharply angled tube. kfactor is a simple measure of the overall rotor efficiency that factors in these variables, where:
A lower kfactor corresponds to a more efficient rotor.
Comparative Efficiencies of Two 70,000 rpm Rotors
Interesting results are obtained when the abovementioned efficiency factors are applied to runs of the Type 70 Ti and Type 70.1 Ti rotors available from Beckman Coulter.
The following example shows how the Type 70.1 Ti rotor at 450,000 x g will pellet the material much more quickly than a Type 70 Ti rotor at a higher RCF (504,000 x g) when both rotors are run at the same rotations per minute (70,000 rpm).
As presented in Table 1, the geometry of the tube cavity in the case of Type 70.1 Ti rotor reduces the rotor’s maximum radius, resulting in a lower gforce, as well as reducing the pathlength of the particles inside the sample tube.
The net effect of this reduced pathlength is a more favorable kfactor for the Type 70.1 Ti rotor, resulting in a pelleting time that is 18% faster than in the Type 70 Ti rotor.
Table 1. Rotor Specifications
Rotor Type

Type 7G Ti

Type 7G.1 Ti

Maximum speed

70,000rpm

70,000rpm

Maximum radius
(r_{max})

91.9mm

82mm

Minimum radius
(r_{min})

39.5mm

40.5mm

Maximum gforce

504,000 x g

450,000 x g

Total pathlength

52.4mm

41.5mm

kfactor

44

36

Bovine serum albumin (BSA) is a protein widely used in research for a variety of purposes. It has a sedimentation coefficient (s) of 4.4s.
For instance, using the previous kfactors calculated (Table 1), if an experimenter employs a Type 70 Ti rotor to pellet BSA, the pelleting time can be calculated as such, where ‘t’ stands for the run time in hours needed to pellet particles of known sedimentation coefficient:
With the help of this basic calculation, researchers can save valuable time and spin the particles for the most efficient duration. When the run time for Type 70.1 Ti rotor is compared with BSA by substituting a kfactor of 36, a time of 8h, 11min is generated, showing that a rotor with a smaller maximum gforce can indeed be more efficient.
Relating Run Time Between Labware
The SW 28 and the SW 32 Ti are popular and highperformance rotors from the Beckman Coulter portfolio.
To compare the run times between two rotors in order to duplicate a certain centrifugation step, all a researcher needs to know is the kfactor of each rotor and the run duration from a previous technique. The following equation can be used for this purpose:
where k_{1} is the kfactor of the SW 32 Ti rotor and k_{2} is the kfactor of the SW 28 rotor; t_{2} is the run duration of a previous method, and t_{1} refers to the unknown spin time for the SW 32 Ti rotor.
This is another simple calculation that aids researchers when comparing techniques between two different centrifuge rotor systems. This equation helps to sediment particles equally and compares efficiency among labware.
As mentioned before, a rotor’s kfactor is determinant upon the pathlength of the standard tube for the given rotor. If a researcher has to use a specific rotor geometry and maximum gforce, it is still possible to improve kfactor by reducing the pathlength.
One such example is the application of Beckman Coulter’s gMax tubes. This novel system uses patented QuickSeal belltop polyallomer tubes and floating spacers.
The gMax spacers, unlike traditional sleeve type adapters, float on top of the tube and the sample is maintained at the maximum radius of the tube cavity  shortening the pathlength of the standard tube for the specified rotor  thereby enabling users to run smaller sample volumes without gforce being reduced.
The duration of the run can be reduced in those rotors where gMax tubes correspond to a shorter pathlength and smaller kfactor, which saves critical time. The gMax tubes can be used with most Beckman Coulter ultracentrifuge rotors.
In Figure 1, the gMax technology shows the significant time savings afforded by using different labware. In the case of the Type 90 Ti rotor, the kfactor of a 4.2 mL gMax tube is 11 compared with a 13.5 mL tube with a kfactor of 25, both spun at 90,000 rpm.
Figure 1 shows an example of gMax technology resulting in a 56% time saving between the two tubes. An overnight spin of 18 h is needed for the majority of applications.
Figure 1. Comparative efficiency of gMax technology
However, equivalent separations are achievable in less than 8 h with the gMax tube, which is more suited to a typical work day and generates a more convenient workflow.
kFactors and LargeScale Vaccine Production
kfactors not only affect the pelleting time of ultracentrifuges, but of all types of centrifuges, as previously mentioned. The example given below shows how kfactor affects the efficiency of rotors in highperformance centrifuges.
The largescale production of vaccines to fight widespread plagues and eliminate diseases worldwide, is critical to the human race. In a large number of cases, highcapacity centrifugation is used to harvest cells, at speeds of about 5,000 x g.
This application has traditionally been carried out in swinging bucket rotors, but high throughput is essential to researchers, to increase yield and reduce the time to market.
Table 2 shows that the JLITE JLA9.1000 and the JLITE JLA8.1000 rotors from Beckman Coulter are welldesigned and reduce the kfactor while processing large volumes in just one spin.
Table 2. Comparison of HighCapacity Fixed Angle 1Liter Rotors
Rotor

JLITE JLA8.1000

JLITE JLA9.1000

Fibrolite™ F96 x

Fibrolite F86 x

Fibrolite F510 x

Fibrolite F66 x

1,000 LEX

1,000y

1,000 LEX

1,000y

Type

FixedAngle

FixedAngle

FixedAngle

FixedAngle

FixedAngle

FixedAngle

Maximum volume (mol)

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 gforce

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 path length (mm)

103.8

103

129

142

151

142

kfactor with largest volume at max speed

2,482

2,540

3,415

5,096

6,662

9,060

The fact that low kfactors correspond with highefficiency saves valuable time and reduces electricity costs and rotor wear.
Also, during the production of vaccines, following the initial cell pelleting step, speeds of 15,000 x g are needed to purify the pathogenic virus antigens, something that both of the 1liter highcapacity rotors from Beckman Coulter are capable of, thereby adding functionality to rotors that are already efficient.
Using Beckman Coulters highperformance rotors, manufacturers can enhance their process performance, shorten time to market, and minimize costs.
About Beckman Coulter
Beckman Coulter develops, manufactures and markets products that simplify, automate and innovate complex biomedical tests. More than a quarter of a million Beckman Coulter instruments operate in laboratories around the world, supplying critical information for improving patient health and reducing the cost of care.
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