Biotechno/. Prog. 1990, 6, 255-261
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Sizing Biological Samples by Photosedimentation Techniques Anton P. J. Middelberg* and I. David L. Boglet Department of Chemical Engineering, The University of Adelaide, G.P.O. Box 498, Adelaide S.A. 5001, Australia
Mark A. Snoswell Bresatec Ltd., Thebarton, South Australia
The performance of the Joyce-Loebl disk centrifuge in the sizing of Escherichia coli cells, protein inclusion bodies, and cell debris is evaluated. The need for a density gradient that extends throughout the entire spin fluid is highlighted, and a set of standard conditions that fulfill this requirement is defined. E. coli cells experience a reduction in their Stokes diameter when exposed to ethanol, indicating that a spin-buffer fluid combination such as glycerol-water is to be preferred for the sizing of bacteria. The instrument baseline is influenced by the presence of particles, and a method of estimating the baseline is described. The sizing of small particles is further complicated by baseline drift due to temperature sensitivity of the optical yoke. An analysis of diffusion in the spin fluid is conducted, and an expression for the sedimentati0n:diffusive flux ratio is derived. For the current samples, it is shown that diffusion within the spin fluid does not lead to significant errors for 0.15-pm particles, whereas the phenomenon may be significant a t the manufacturer’s size limit of 0.01 pm.
Introduction Downstream processing in biotechnology has traditionally received less research attention than the area of fermentation, although it is now recognized that in some instances downstream processing costs may dominate and control project viability (Allen, 1988). The required downstream operations will be dictated by the nature of the product, which may be expressed either in a soluble form or as an insoluble protein inclusion body (Hoare and Dunnill, 1986a,b; Kane, 1988; Marston, 1986). In the former case, centrifugation may be employed to sediment cell debris from the product stream (Aronsson and Zadorecki, 1987), whereas the aim in the latter case will be to sediment the inclusion bodies while losing as much cell debris as possible to the supernatant stream (Middelberg et al., 1989). Centrifugation is also commonly used for cell harvest prior to disruption (Aronsson and Zadorecki, 1987). The mathematical modeling of disk stack centrifuges, the most common centrifuge type employed in biotechnology, has progressed to the point where the hydrodynamics of the flow between disks has been characterized and individual particle motions may be calculated (Bohman, 1974; Gupta, 1981). Simplistically, centrifuge performance will be dictated by the particle settling velocity, the centrifuge feed rate, and the machine design. For small particles the settling velocity will be the Stokes velocity corrected for hindered settling effects:
where k will be a function of centrifuge feed concentration. Centrifuge models usually include the above expression, t Present address: Department of Chemical and Biochemical Engineering, University College, London, U.K.
8756-7938/90/3006-0255$02.50/0
indicating that the particle diameter is an important physical parameter which must be determined. Many techniques are available for size determination, but these generally lead to diameters that are not representative of the Stokes diameter because of shape and surface roughness effects. For example, microscopic sizing of rod-shaped bacteria will lead to a diameter and length, which must subsequently be translated into an effective Stokes diameter. A more appropriate sizing technique is one that will explicitly give the particle Stokes diameter or, better still, the single-particle settling velocity, u. The Joyce-Loebl DCF4 disk centrifuge (Joyce-Loebl Ltd., Gateshead, U.K.) fulfills this requirement and has previously been used to size protein inclusion bodies (Taylor et al., 1986). This paper evaluates the performance of this instrument, with special emphasis on the sizing of whole Escherichia coli, protein inclusion bodies, and cell debris. The principle of operation of the disk centrifuge is outlined, and theoretical considerations are dealt with. A data reduction system is briefly described, and finally, results of tests conducted with the disk centrifuge are presented and discussed.
Principle of Operation The Joyce-Loebl particle size analyzer operates by using the principle of sedimentation (Joyce-Loebl, 1985). With reference to Figure 1,a rotating disk is loaded with “spin fluid” and then the sample, containing the particles, is layered onto the inner radius of this annulus. All particles thus start at nearly the same radius and experience a net centrifugal force due to the rotation of the disk. The diameter of a particle at the detector will be given by eq 2 (Taylor et al., 1986). If the amount of material reaching the detector can be determined as a function of time, the size distribution of the sample may be determined. The disk centrifuge uses
@ 1990 American Chemical Society and American Institute of Chemical Engineers
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-
Time Zero
However, absorbance is defined as (Oppenheimer, 1983)
Time t
Disc Rotation
Disc Rotation
A Fluid & Sample
Lfl to Outer wall
Figure 1. Schematic diagram of the Joyce-Loebl disk centrifuge.
L
a nonintrusive method, by measuring the absorbance of the spin fluid at the detection radius as a function of time. The problem, dealt with in the next section, is then to relate this measurement to the sample size distribution.
Theoretical Considerations The Particle Extinction Coefficient. Ideally, when placed in a light path, a particle will obscure an amount of light that is proportional t o its projected crosssectional area. However, this ideal behavior ceases to hold when the particle size approaches the wavelength of light (Allen, 1968a). This breakdown of the laws of geometric optics is accounted for by defining the particle extinction coefficient, K , as light obscured by the particle (3) light that would be obscured ideally Using Mie theory, Allen (1968a) derives functional relationships for the extinction coefficient for several cases, including those of a totally reflecting and a nonabsorbing sphere. The practical application of such equations requires a knowledge of the optical properties of the test sample. Brugger (1976) suggests an experimental method for determining the particle extinction coefficient. The technique requires a cumulative size distribution of the particles, which is obtained by fractionating the sample at a predetermined size parameter (the equivalent Stokes diameter) and analyzing the under- or oversize fractions calorimetrically. The technique is, however, extremely time-consuming and therefore not suitable for biological samples that degrade rapidly with storage. Oppenheimer (1983) provides a relationship for the extinction coefficient for polystyrene in water, which was used previously to size inclusion bodies (Taylor et al., 1986). Equation 4 has been fitted to the curve for white light to facilitate data reduction in the current study.
K=
K = 3.25D2*55
D I0.5 pm (4) D 2 0.5 pm An example of the effect of the extinction coefficient on the measured particle size distribution is given by Statham (1972). Interpretation of the Disk Centrifuge Output. Treasure (1964) presents an analysis which indicates that the disk centrifuge will yield a distribution by particle volume. The following equation is given relating absorbance and particle diameter, with the assumption of a constant extinction coefficient, K':
K = 3 0 - 0.945
A = ND2DK'
(5)
N D ~
(6)
so that a size distribution by particle cross-sectional area should be obtained if the disk centrifuge output, corrected by the extinction coefficient, is plotted against the particle diameter as given by eq 2. This is supported by Allen (1968b), as a t any time there is only a very narrow distribution of particles in the path of the detector. From eq 6 we may write, in the region of a linear variation of extinction coefficient with particle diameter A =N D ~K D(~) (7) where the term in parentheses will be a constant and equivalent to K' in eq 5. Treasure's analysis is therefore an approximation to eq 6, so a plot of the group DA Y ' K against the particle diameter should represent the sample size distribution by volume. Such a plot may be integrated to give the cumulative undersize curve, defined as (9)
Diffusion in the Disk Centrifuge. For eq 2 to be valid, the driving force for the sample must be predominantly sedimentation. The manufacturers of the disk centrifuge state that the machine is capable of analyzing particles down to 0.01 pm depending on the specific gravity of the sample (Joyce-Loebl, 1985). A t any time t , a concentration profile will exist in the centrifuge disk due to the different sedimentation rates of particles of different size. This concentration profile can be evaluated in terms of the particle size distribution by using eq 2 . Given this concentration profile, the diffusive flux a t any radius in the spin fluid can be calculated at any time since test commencement. With these concepts in mind, the following equation for the ratio of sedimentative to diffusive flux in the spin fluid annulus may be written (see supplementary material):
-J s_ -
.lrApD3r2u2
The flux ratio can therefore be determined as a function of particle diameter and radius in the spin fluid, which can be related to the time since sample injection by eq 2. Equation 10 employs the method of hypothesis testing to determine whether a given sample can be accurately sized by the Joyce-Loebl disk centrifuge for a specific set of operating parameters. Given the hypothesis that diffusion is insignificant, a concentration profile can be determined and the flux ratio for a given particle size calculated at any time since sample injection (= location in spin fluid, eq 2). If the flux ratio indicates that diffusion is significant, a new set of operating parameters can be selected and the hypothesis retested. Furthermore, eq 10 gives the relationship between the key variables, thus facilitating the selection of new operating conditions. By using eq 10, a given sample can be evaluated to establish whether eq 2 is valid. Consider, for example, a
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70000
1
A 35000
0 I ' 0
900
600
300
Time [secs) Figure 2. Baseline instability: effect of unstable boost conditions. Table I. Data for Eq 2 spin fluid viscosity (cP) specific gravity
water
10% glycerol
1.14 0.994
1.36 1.016
monodisperse sample. The differential of the frequency distribution ( d y / d D , eq 10) will be infinite, and consequently the flux ratio will tend to zero. The effect of diffusion on the measured particle size distribution must therefore be accounted for. In practice, so-called monodisperse samples are likely to be distributed with very small standard deviations (e.g., 10-1296; Wachtel and La Mer, 1962). Clearly, while the differential of the frequency distribution will be large for such samples, it can be compensated for with higher rotational speeds. For many biological samples with broad size distributions (small dy/ dD), diffusion should be insignificant. Note that eq 10 does not take into account the initial diffusion transient due to the concentration discontinuity at ro. Hence, it should not be used in the limit as r ro. In most practical situations, the transient will be quickly damped, and eq 10 may be applied after the system has stabilized. -+
Data Reduction The disk centrifuge outputs an analog signal that can be directly sent to a chart recorder. In the current tests, data were sampled by an IC1 Consort I1 analog-digital converter a t 1-s intervals and sent to a DOS-based computer. Within the DOS environment, the data could be corrected for the extinction coefficient by using eq 4, and a plot of y (eq 8) against Stokes diameter (eq 2) could be generated. Alternatively, raw data could be presented as a plot of A against time. All tests were carried out with either 10% (w/w) glycerol-water or water spin fluids, with water and 20% (v/v) ethanol-water buffer fluids, respectively. The data summarized in Table I were used to calculate the Stokes diameter by eq 2 and are for mixtures of 90% spin fluid with 10% buffer fluid. Spin fluid densities were determined by using volumetric flasks. Viscosity measurements of the spin fluid were done at 20 "C with a Brookfield LVT cone-and-plate viscometer at a shear rate of 450 s-l.
Results and Discussion The Density Gradient. One of the major problems to be overcome with the disk centrifuge is streaming (Joy&Loebl, 1985). Lowering of the sample concentration has been successfullyused to combat streaming (Taylor et al., 1986), although this has the disadvantage of making detection very difficult. Brugger (1976) addresses the problems of instability in a disk centrifuge and suggests that a spin fluid density gradient sufficiently large to overcome all disturbing influences is necessary. It was suggested that stable sedimentation is obtained only in the region of the density gradient and that, under the conditions of a successful run, the density gradient extends throughout the spin fluid. A density gradient can be established by layering a "buffer fluid" with a lower density than the spin fluid on the annulus and then mixing it into the annulus by temporarily accelerating the disk with the machine boost action (Joyce-Loebl, 1985). By loading ink into the buffer fluid, it could be seen that the following two problems could be associated with unsuccessful runs for both types of spin fluid evaluated: (a) With insufficient boost, the density gradient extends to a certain point within the spin fluid annulus and then stops. Settling particles behave well until this abrupt density discontinuity is reached and then begin t o turbulently mix into the rest of the spin fluid. This may explain the phenomenon of secondary streaming described by the manufacturer (Joyce-Loebl, 1985). (b) Also with insufficient boost, a condition where the density gradient is not stable can arise. This leads to continued mixing between the buffer layer and the spin fluid during the course of the test. Mixtures containing different quantities of ethanol and water will possess different refractive indices, so that any variation in the composition of the spin fluid at the detector will result in a variation in the baseline. The second phenomenon is clearly illustrated in Figure 2, which is a plot of the raw machine output as a function of time. Each plot represents the machine baseline at 8000 rpm, obtained by using the following procedure: t=O
t = 180 s t = 200 s
Inject 20 mL of water spin fluid. Begin data collection. Inject 1 mL of 20% (v/v) ethanol in water. Give three boosts with the boost button set to 80. The machine is allowed to resynchronize itself before the next boost action.
The three peaks at approximately 200 s in Figure 2 correspond to depression of the boost button. The variation in refractive index is clearly shown, the difference in the two plots perhaps being attributable to slight variation in the boost action. By use of ink tracers, the conditions, given in Table 11, that give a stable density gradient were determined for the two spin fluids. The time lags between each successive boost action were determined such that stability within the spin fluid had been achieved prior to the next action. The schemes are reproducible and provide a straight baseline as shown by Figure 3. Sample injection would occur at 300 s, the peaks prior to this time being attributable to the boost action. Baseline Drift Due to Temperature Effects. Baseline drift at long spin times was noted, which was initially attributed to refractive index variations but was later identified as temperature sensitivity of the optical yoke. The manufacturer was queried regarding the temperature sensitivity and responded with a drift check, which was successfully carried out, an allowable drift of *2.8% / h of
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Table 11. Standard Conditions spin fluid
water disk speed (rpm) machine gain spin fluid volume (mL) buffer fluid buffer fluid volume (mL) sample suspended in sample volume (mL) sample concentration t=Os
t=60s t=90s t = 150 s t = 210 s t = 300 s
70000
10% glycerol 8000 6.0 20.0
8000 6.0 20.0
20% (v/v) ethanol water 1.5 1.5 20% (v/v) ethanol water
A 5000
0.5
0.5
