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The Field-Flow Fractionation principle

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1 The Field-Flow Fractionation principle
Sample introduction External field Length Flow Thickness Breadth Field-flow fractionation (FFF) is a family of separation techniques which are able to fractionate a broad range of macromolecules, nano- and micro-sized particles. It has been commonly referred to as “one-phase” chromatography since it uses a liquid mobile phase as in liquid chromatography. Nonetheless, the separation is structured inside a channel without stationary phase by the action of a field or gradient that is applied perpendicularly to the direction of the mobile phase flow. Classical FFF devices have been based on a flat, rectangular-shaped channel with capillary cross-section. Across the channel section the mobile phase profile is parabolic, as in capillary gas chromatographic columns. Typical channel dimensions are cm in length, 2 cm in breadth and micrometers in thickness. We can have different type of fields that define the different FFF variants which can be, consequently, applied to different type of samples. Detector Thickness Sample Parabolic flow

Field-flow fractionation is a family of chromatographic-like techniques suited to separating macromolecules, nano-sized and micro-dispersed particles in liquid phase. Separation is based on size, shape and surface properties. Retention is obtained, rather than by the interaction with a stationary phase, through an external field applied perpendicularly to the mobile phase flow. The origin of the applied field (gravitational, centrifugal, hydrodynamical, electrical, magnetical, thermal) sorts the different FFF subfamilies. This slide shows some applications of the FFF subtechniques. Flow FFF and centrifugal sedimentation FFF are the most widely used FFF techniques. They’ve been applied to samples spanning more than 15 orders of magnitude in molecular weight. Among samples of biological origin, proteins, protein complexes, micro-organisms and cells have been separated and characterized. Gravitational FFF is a simple subset of sedimentation FFF, which uses the Earth’s gravity as the external field. The intensity of such a field restricts the applicability o GFFF to particles larger than about 1 micron. However, GFFF has been successfully applied to several samples, among which cells, yeast and bacteria, with considerable advantage in terms of instrumental simplicity. The instrumental set up of an FFF system can be derived from a standard liquid chromatograph by simply replacing the column with the fractionation cannel. In order to explain the principles of separation, in the next slide we show a scheme of the channels for the two subtechniques used in this work, the flow and gravitational FFF.

3 FFF retention in normal mode
Field x Flow <v> w l C(x) C0 é ù x æ 2 x ö Flow V = 6 < v > ê - ç ÷ ú ê w è w ø ë ú û - c = x / l ( x ) c e Field

4 Basic theory in normal FFF
ú û ù ê ë é ÷ ø ö ç è æ - > < = 2 6 w x v V ( ) c x = c e - x / l Mean layer thickness Retention l D V V é 1 ù l = = R = o = = 6 l coth - 2 l @ 6 l ê ú w Uw V < v > ë 2 l û r kT D = 6 ph r F = fU Potentially ABSOLUTE TECHNIQUE kT l = Fw

5 FFF retention in reversed mode
Field Flow Lift forces d w x In figura vediamo schematizzato il canale attraverso il quale avviene il frazionamento in GrFFF. Il flusso di eluizione entro lo spessore del canale è governato da leggi idrodinamiche, che ne prevedono un profilo parabolico, mentre il fenomeno della ritenzione è basato sul campo gravitazionale terrestre: sotto l’influenza del campo esterno le particelle di campione tendono a depositarsi sul fondo del canale, ma esistono forze di sollevamento che agiscono in opposizione al campo, cosicché per ogni particella si instaura un equilibrio ad una certa distanza d dalla parete, che dipende dalle dimensioni della particella stessa. In questo modo vengono eluite per prime le particelle più grosse, che interagendo maggiomente sono più sospinte verso il centro del canale dove il flusso di eluizione è più veloce. Il rapporto di ritenzione R può essere messo in relazione con la dimensione delle particelle in due modi: o mediante questa prima relazione, in cui a rappresenta il raggio idrodinamico medio della particella e w è lo spessore del canale, che prevede il calcolo del parametro di correzione g mediante il modello semiempirico PSAD, da noi elaborato, che illustrerò tra poco. Un secondo modo per ottenere la conversione della ritenzione in una scala di diametri è tramite questa seconda relazione in cui t0 rappresenta il tempo morto e tr1 corrisponde al tempo di ritenzione di una particella di diametro unitario. Questo metodo prevede la determinazione della selettività Sd come pendenza della regressione lineare del logaritmo dei tempi di ritenzione contro il logaritmo dei corrispondenti diametri. Anche tr1 è ottenibile come intercetta dalla stessa retta da cui ricaviamo la selettività, mentre t0 è un dato sperimentale. a æ a ö t log V = = R 6 g ç 1 - ÷ R = r d S S ç d d log d w t è w ø r 1

6 Selectivity and Resolution in FFF
Normal mode Normal mode Normal mode Normal mode Normal mode Normal mode St/Hyp mode St/Hyp mode St/Hyp mode St/Hyp mode St/Hyp mode St/Hyp mode S d V M r = ln Sd Sd Sd Sd FFF FFF S= 1 S= 1 S= 1 S= 1 FFF FFF 1.0 1.0 1.0 1.0 1.0 1.0 Resolution ) ) ) ) dlnM dlnM dlnM dlnM S= 0.6 S= 0.6 S= 0.6 S= 0.6 R N s = 4 D / / / / R R R R ThFFF ThFFF ThFFF ThFFF dlnV dlnV dlnV dlnV Transit. Transit. Transit. Transit. 0.5 0.5 0.5 0.5 0.5 0.5 FlFFF FlFFF FlFFF FlFFF zone zone zone zone Selectivity ( Selectivity ( Selectivity ( Selectivity ( S S S S = 0.9 = 0.9 = 0.9 = 0.9 d d d R N d V M s r = 4 ln D d GrFFF S= 0.1 S= 0.1 S= 0.1 S= 0.1 SEC SEC SEC SEC k ' 1 + k ' 1 + D K D K Efficiency Selectivity 3 3 3 3 3 3 5 5 5 5 5 5 7 7 7 7 7 7 9 9 9 9 9 9 11 11 11 11 11 11 13 13 13 13 13 13 15 15 15 15 15 15 17 17 17 17 17 17 Log MW Log MW Log MW Log MW

7 Gravitational FFF Sample Sample outlet Injection valve Clamping frame
Spacer Channel wall More than a decade later, Chmelík et al. employed gravitational FFF (GFFF) to sort mouse bone marrow stem cells that were re-transplanted after irradiation. The gravitational channel we have used can be easily home-built at a very low cost. The channel is in fact an empty ribbon-like capillary, in our case 30 cm long. It is cut out from a thin plastic foil called spacer. In our case the thickness is 140 micrometers. The spacer is sandwiched between two plastic or glass bars. The channel operates in horizontal position, to allow Earth’s gravity to act perpendicularly to the mobile phase flow stream.

8 GrFFF of E.coli Sample: CS5 0398 (fimbriated)
Number of cells/mL in the 1:1 sample = Sample: CS (non-fimbriated) Number of cells/mL in the 1:1 sample = Carrier: 80% 0.05% w/v SDS, 0.01% w/v NaN3 20% MeOH Detection: UV-Vis 600 nm; 260 nm Injection volume: 20 µL Injection flow rate: 0.2 mL/min Injection time: 25 s Stop flow time: min Elution flow rate: mL/min CS (non-fimbriated) Bacteria analysis by separation methods is of great interest since bacteria are used in diverse fields as biomedical applications, biotechnology and, unfortunately, biological warfare. Also the ability to distinguish living or dead bacteria is important. Deactivated bacteria are of biotechnological interest for whole-cell vaccines. For more than two decades E.coli has been the workhorse of biotechnology. These bacteria form part of the natural human gastrointestinal tract flora. However, they can often cause infections. So, interest in immuno-prophylaxis against the infections caused by pathogenic E.coli is increasing. E.coli can differ with regard to the presence of fimbriae on the bacterial surface. Fimbriae affect the immuno-response and so the use of E.coli for whole-cell vaccines. In can be therefore interesting to sort fimbriated/non fimbriated E.coli strains, as shown here by HF FlFFF. The two different strains of fimbriated/non fimbriated E.coli can be completely separated and distinguished by HF FlFFF. In this case and for all the cases shown in the next slides, HF FlFFF operates in reversed mode, because of their supra-micron size of cells. CS (fimbriated)

9 E.coli sorting by GrFFF Elution flow rate = 0.3 mL min-1
5 10 15 20 (1) (2) Detector Response Retention time (min) Elution flow rate = 0.3 mL min-1 Stop-flow time= 15 min (a) Fimbriated CS5 0398 (b) Non fimbriated XC113A2 (c) Non fimbriated CS Repeated runs reported for each case Fimbriated CS5 0398 (1) cells (2) cells (b) Detector Response (c) Non fimbriated 0.3 mL min-1 0.6 mL min-1 (a) 10 20 30 40 Retention time (min)

10 Chemiluminescence detection in GrFFF
High signal/mass ratio Long-lasting emission (glow kinetics) Horseradish peroxidase (HRP) luminol N H 2 O , - HRP C + light Chemiluminescence detection allowed to achieve very high sensitivity (and specificity) in particular when it is used for the detection of enzymes. In fact, enzymes suitable for CL detection, such as that used in our experiments (horseradish peroxidase and alkaline phosphatase), are characterized by very high signal/mass ratios and, in the presence of an excess of substrate, produce a stable CL signal, which is very useful from an analytical point of view. In our experiments we used two common enzymes suitable for chemiluminescent detection. NOTES: Detection of horseradish peroxidase (hereafter indicated as HRP) is based on the chemiluminescent oxidation of luminol, which is catalyzed by this enzyme in alkaline medium. This reaction gives the product, the 3-aminophthalate ion, in an electronically excited state, which thus decay to give the molecule in the ground state and a photon. The other enzyme is the alkaline phosphatase, hereafter indicated as AP. Detection of AP is commonly based on 1,2-dioxetane chemiluminescent substrates. These substrate are dephosphorilated by the enzyme, giving an unstable intermediate that decomposes giving light emission. Alkaline phosphatase (AP) 1,2-dioxetane O M e P 3 -- AP - C + light H 4

11 Enzyme-coated particles
Where is CL localized? 3-aminophthalate + light excited 3-aminophthalate intermediate products H 2 O HRP 2 H O PS luminol This slide shows a simplified scheme of the reactions that lead to the chemiluminescence emission in the case of HRP. Decomposition of luminol takes place in solution. When CL is applied to the detection of particles, one of the problem to be considered is that the CL signal actually is obtained from a shell of solution around the bead, and not directly from the bead surface. Actually, the CL signal is localized on the PS/HRP beads only if the lifetime of the excited product emitting light is shorter compared to its diffusion rate! HRP-catalyzed oxidation of luminol CL emission takes place in solution: the CL signal is localized on the enzyme-coated beads if the lifetime of the excited, CL-emitting product is shorter compared to its diffusion rate

12 Mobile phase with CL substrate
In situ GrFFF-CL Instrumental layout Slow-scan, ultrasensitive cooled CCD camera for sequential image acquisition CCD Pump 0.75 GFFF channel We have examined the possibility to develop an on-line CL detection in FFF. To avoid band-broadening effects due to the use of a post-column detection system, we added the CL substrate directly to the mobile phase in order to obtain the CL signal during the elution of the sample. To develop this system we have used the gravitational FFF subtechnique, GFFF. Because of its simplicity, GFFF is very suitable to the addition of the chemiluminescent cocktail directly into the mobile phase. We have just to recall that CL substrates are generally unstable, so that their reaction can be catalyzed by other components of the system, other than the analyte. We have first used a low-light luminograph to detect the CL emission. We put the GFFF In this way, we can obtain frames showing the spatial distribution of the sample within the FFF channel. Mobile phase with CL substrate Injection valve CL substrates in the mobile phase to reduce extra-column band broadening CL images collection: visualization of the fractionation of free/particle-bonded analytes

13 In situ GrFFF-CL Real-time imaging of the analyte fractionation
Channel inlet Direct analysis of sample relaxation Direct evaluation of sample recovery and particle wall-interactions Injection Information on the fractionation process from band profiles  optimization and kinetic studies This is an example of what we can get from the CL images obtained with this system. Images show an upper view of the GFFF channel during the elution and relaxation processes. To obtain this views, CL images were processed and converted to pseudocolors, showing from green to red the different intensities of the CL emission. Real-time imaging of the injection procedure can allows to optimise the system. The development of sample bands along the channel gives accurate information on the kinetic of the fractionation. At the and of the sample elution, total recovery can be directly evaluated from the residual luminescence of the channel. Direct analysis of non-ideality effects Elution

14 In situ GrFFF-CL Real-time imaging of free HRP + PS/HRP fractionation
Sample: 1.25 ng HRP e 7.5 mg PS/HRP 6 mm Several pictures taken during an FFF-CL experiment have been put together into a movie, that clearly illustrates the separation process. In this case, the sample was a mixture of free HRP and PS/HRP, which has been injected at the left end of the channel. Free HRP is not affected by the gravitational field and elutes at the void time. On the other hand, the particles are retained, so that the two bands are completely separated. The yellow line shows the evolution of CL signal along the channel, with the two bands eluting at different velocity. We also generate the signal as it were from a flow-through CL detector at the end of the channel by the integration of the CL intensity measured at the end of the channel as a function of time.

15 FFF a campo idrodinamico (FlFFF)
Flusso in ingresso nel canale (iniezione del campione) Flusso trasversale Flusso in uscita dal canale (al rivelatore) Plexiglass Frit poroso Spacer Membrana opzionale Frit poroso Plexiglass Flusso trasversale

16 Sistema FlFFF Canale FlFFF

17 parete di accumulazione
Meccanismo FlFFF flusso trasversale flusso trasversale flusso di campione in entrata flusso di campione in uscita profilo parabolico A B C parete di deplezione parete di accumulazione (membrana opzionale) flusso trasversale in uscita Ritenzione in FlFFF La ritenzione dipende solo dalle dimensioni

18 FlFFF in modo normale Separazione di 3 lattici PS
Condizioni sperimentali V = 1 . 98 cm / min 3 V = . 70 cm / min c 0.08 V0 = 1.11 mL 155 nm w = . 02 cm 3 t0 T = 298 K 0.06 Turbidità 54 nm 0.04 102 nm 0.02 0.00 5 10 15 20 tr [min]

19 Reversed FlFFF-CL Injected sample:
mixture of PS/HRP 6/3 mm and PS 10/4 mm 5 mg PS/HRP 6 mm + 5 mg PS/AP 3 mm We can also get multianalyte detection if we exploit the high size-based selectivity of FFF. The high specificity of FFF-CL is shown in this slide. The first plot shows the fractograms obtained for in flow FFF for a mixture of four PS particles of different size. The two particles of 3 and 6 microns are coated with linked-HRP while the two particles of 10 and 4 microns are uncoated. If we compare UV and CL fractograms we can clearly see that CL is able to specifically detect the HRP-coated particles, and uncoated particles give no signal. The second plot shows that we can selectively detect separated particles of different size coated with different analytes. In the sample here we have mixed 6 micron PS coated with linked-HRP with 3 micron PS coated with linked AP. In red we have the non selective UV trace. The line in ciano is the CL fractogram obtained after the addition to the collected fractions of the specific substrate for the CL detection of AP, while the line in yellow is the fractogram obtained after the addition of the specific substrate for the CL detection of HRP. This is a proof of the applicability of FFF-CL to multi-analyte detection, based on different CL-catalyzing enzymes coated on particles of different size.

20 Hollow-Fiber FlFFF: miniaturization
Flow Flow Field 1/8” PE fitting 1/8” PE Tee 1/8” Teflon tube The idea of hollow fiber membranes as microcolumn channels for FlFFF was reported since However, high performance HF FlFFF of particles has been shown only recently by our Korean coworkers, through the optimization of the HF FlFFF channel and system design. In HF FlFFF sample separation is structured by the force generated by the radial flow through the porous wall of the HF membrane. In HF FlFFF the flow that is inlet into the HF channel is divided into two parts: part of the flow penetrates the HF inner wall as radial flow and the rest exits along the HF as axial flow. The microcolumn channels we have developed are made of polysulfone or chlorinated polyvinylchloride HF membranes. The HF dimensions are 24.0 cm in length and cm in nominal, inner radius. The HF is inserted into two pieces of 1/8” Teflon tube with a tee connection for the radial flow exit. Two 1/8” PEEK ferrules are used for the channel inlet and outlet connections to the system. The key advantage of this type of HF FlFFF channel clearly lies in its simplicity, low-cost and miniaturization, if compared to classical FlFFF systems. These features allow for disposable usage of HF FlFFF. Disposable separators can be particularly appealing for analytical and micro-preparative scale bio-separations, in which either sterility or run-to-run reproducibility are critical. cPVC / PSf HF membrane 24x0.08 ID cm 1/8” PEEK ferrule 1/8” PEEK ferrule

21 HF FlFFF in normal mode Flow Field z L rf C(z) C0 x U > < v l
Let’s now move on to some basics on retention in HF FlFFF. In HF FlFFF we can have two retention modes. The first mode, which is called normal or Brownian mode, operates for submicrometer-sized particles. The sample components of small diameter have higher Brownian diffusion coefficients. By the action of the radial flow they reach an equilibrium position from the fiber wall that is located further away than sample components of bigger size that have lower diffusion coefficients, and they elute first. Therefore, the elution order follows up the increase in particle size. Let’s define Vin, Vout and Vrad the inlet, outlet and radial flow rates, <v> the average velocity of the mobile phase, rf the fiber radius, U the cross-flow velocity at the fiber wall, l the mean sample band thickness across the fiber, L the channel length, z the radial axis, C0 the sample band concentration at the inner wall of the fiber. rf Flow l C(z) > < v C0 x U Field

22 HF FlFFF in reversed mode
In HF FlFFF, however, we can have another type of retention mechanism. Micron-sized particles reach their position across the HF channel section because of steric effects. In fact, their Brownian diffusion is negligible. On the other hand, the longitudinal laminar flow generates on the particles opposite forces, known as lift forces. SAME MECHANISM DESCRIBED FOR GrFFF This way, particles actually tend to be lifted away from the accumulation wall to migrate at a position that is elevated from the channel wall, at which they are focused as narrow layer (hyperlayer). Larger particles this way get faster streamlines of the parabolic flow profile than small particles do, so they are then swept down the channel earlier. The elution mode is, in fact, reversed with respect to the elution of sub-micrometer-sized particles, and the relevant retention mechanism is called steric/hyperlayer, or focusing. rf Flow Lift d Field

23 HF FlFFF retention rf d R 4 l + 2 g  Normal/reversed mode Normal mode
In normal or reversed HF FlFFF, retention is related to the particle diffusion coeffient or size through a simple expressions. In reversed mode, however, the hydrodynamic correction factor cannot be predicted from theory. We can get particle size from calibration with standards of known size by the measurement of the size-based selectivity obtained under given experimental conditions. If from the linear regression of log tr vs. log d of standards we measure the slope (Sd) and the intercept (tr1), we can then easily obtain the size of our sample. From the slope and the intercept we can also determine the size at which the transition from normal to reversed mode turns up. This way, we can obtain the general expression for retention as a sum of the two different terms which holds true in normal and reversed mode. Typically, the inversion diameter lies in the range micrometers, depending on the flow rate values. rf d R 4 l + 2 g

24 FO LP UV/Vis/DAD Focusing lens Fiber optic Mirror guide Revolver
filter Beam combiner Light pipe cell Deuterium lamp Tungsten lamp Let us now come to detection issues. This detector we have used for HF FlFFF of cells is a light-pipe detector cell is able to enhance the general performance of HF FlFFF, by reducing not only HF deformation with usage but also the limit of detection and, then, the sample load. We have used for this work the ThermoFinnigan UV 6000 DAD for its highly-sensitive 5 cm light-pipe cell with low backpressure. NOTES Cell pathlength was measured with a spectroscopic standard, as described in previous work. It resulted to be 4.6  0.3 cm. Channel life-times were not significantly different from those of HF channels in cPVC and PAN (ca. 30 runs). Mod. TSP UV 6000 LP Diode Array Fixed Grating

25 Instrumental output: Fractograms and spectra
HF/FlFFF-FO/UV/DAD of Vibrio cholerae Instrumental output: Fractograms and spectra Contour plot void Spectrum at the peak maximum V. cholerae Fractograms at 3 different wavelengths 3D plot

26 HF FlFFF of V. cholerae UV/Vis signal (mAU) tr (min) Void
Membrane: PSf 30,000 Da Serotypes: Inaba, Ogawa Injected cells~ (in 5 µl) Mobile phase: FL % NaN % Focusing time: 3 min Vrad = 51 µl/min Vin = 1.5 ml/min UV/Vis signal (mAU) I want to start by showing HF FlFFF-based sorting of deactivated V. cholerae used for whole-cell vaccines. Deactivated V. cholerae are sub-micron sized, rod-shaped bacteria with tail. It is important to note that the submicron size of these V. cholerae strains did not allow to sort them by flow cytometry, the most common technique nowadays for cell sorting. It is shown here that it is possible to obtain high performance HF FlFFF of V. cholerae at quite short analysis time. The two serotypes Inaba and Ogawa can be also partly distinguished by the elution profiles. Reproducibility was also tested since it’s been always a major concern in HF FlFFF even when standard samples are used. Run-to-run reproducibility of HF FlFFF of V. cholerae is shown here to be good, as indicated by the superimposed fractograms obtained with repeated runs. tr (min)

27 HF FlFFF of HRBC Recovery and Detectability
Void Membrane: cPVC 30,000 Da Mobile phase: Isotonic PBS (300 mOsm) Cholic acid 1mM Vin = 3.00 ml/min Vrad = 0.27 ml/min Injected cells: 70,000 Area = min Recovery = 68% 7,000 Area = min Recovery = 78% Due to the very critical choice of surfactant, we have first performed sample recovery studies to test quantitative performance of HF FlFFF for cells….. ….. and the results are here shown. Absolute recovery can be evaluated by the ratio of the band area values obtained for in-channel and off-channel injections of the same number of cells. Linear recovery can be determined by the evaluation of fractogram area values obtained for the injection of different numbers of cells. In order to determine the absolute recovery, the same number of HRBCs injected to obtain the fractogram in red was also injected off-channel. The absolute recovery results to be relatively high: 78% of the 7,000 injected HRBCs. From the ratio between the area values of the (a) / (b) fractograms , non linear recovery is however observed: (a) 68% recovery of 70,000 HRBCs; (b) 78% recovery of 7,000 HRBCs. Otherwise, this finding may indicate that the lower the number of injected cells, the higher the absolute recovery. However, the obtained values of recovery are acceptable, particularly if it is considered that the possible disposable usage of the channel does not induce the risk of sample carry-over. NOTES The 600 nm wavelength was chosen for the quality of the signal and also to keep far for the absorption zone of biological macromolecules contained in the HRBCs ( an absorption peak near 400 nm was observed, superimposed to the scattering spectrum). injected mass about 200 pg. original sample concentration: cells/ml. Fresh human blood was drawn from donors under clinical control. Samples were collected in EDTA-containing tubes to inhibit coagulation. A 2-fold dilution was then performed in isotonic PBS (150 mM, pH=7.4) and samples were stored at 4 °C. They were analyzed within 4 days after further 1500150-fold dilution in the chosen mobile phase. HRBCs were injected in a range of 7,00070,000 cells for each run. Certified determination of average HRBC concentration and average HRBC number distribution were obtained for all blood samples by standard methods of clinical analysis

28 HF FlFFF of winemaking yeast
Void Membrane: PSf 30,000 Da Mobile phase: FL % NaN % TRIS 0.125% Focusing time: 6 min Vin= 3 ml/min Vrad= 0.44 ml/min PS standards Sd=1.50±0.10 S. cerevisiae HF FlFFF-based size=4.8±0.3 µm S. cerevisiae Here we have fractionated and sized by HF FlFFF a strain of winemaking yeast. Although S. cerevisiae is not spherical we have anyway measured the size-based selectivity with the PS mixture shown in this slide. Regression gives Sd=1.50±0.10, a pretty high value from which we get the hydrodynamic diameter of the yeast cells as 4.8 ± 0.3 um. This value is comparable to the cell size of other types of winemaking yeast previously determined by us with the use of a non separative method like Coulter counter. NOTES Commercial, dry winemaking yeast cells (Saccharomyces cerevisiae) were resuspended for one hour in ultrapure water. Samples were stored at 4 °C and then diluted in the mobile phase before the injection of approximately 100,000 cells. Active dry wine yeast is currently employed as a starter for commercial wine production. SdFFF showed suitable to monitor the growth of yeast cells by fractionation after cultivation [43]. Sanz et al. have recently employed GFFF to fractionate and distinguish different types of commercial, dry winemaking yeast from S. cerevisiae [27,28]. In Fig. 6 it is reported HF FlFFF of a commercial strain of dry winemaking yeast from S. cerevisiae. The HF membrane used was PSf 30,000 Da. The fractogram of a mixture of PS obtained at the same flow rate conditions used for the yeast sample is superimposed in Fig. 6. These flow rate conditions were those employed for the regression analysis with PS discussed in section 4.1, from which Sd=1.5  0.1. From this Sd value one gets (Eq. (4)) the hydrodynamic diameter of the yeast cells as 4.8±0.3 m. Although yeast cells cannot be considered as perfectly spherical, this value is comparable to the cell size of other types of winemaking yeast from S. cerevisiae, which has been determined by the Coulter counter measurements performed in previous GFFF of winemaking yeast [27,28]. It is noteworthy that HF FlFFF shows here, with quite shorter analysis time, a fractionation performance that is, at least, comparable to that obtained in SdFFF or GFFF of yeast cells

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