Electrophoresis 1990, 11, 907-912
Preparative isoelectric focusing
erature only gave satisfactory results for a limited range of parameters. In contrast, the method reported here has no restrictions of this kind. The computational procedure was constructed on the basis of our previous theoretical analysis. The convergence of iterations is theoretically assured and the only restriction to accuracy is the cumulation of round-off errors. The method provides a basis for estimating the errors due to theelectroneutrality approximation. For the threeexamples considered here, these errors d o not exceed 0.02 %, with larger errors corresponding to the largest value of E=O.O 1.Therefore, we can state that the electroneutrality approximation can indeed be used in those three cases. Received June 5, 1990
Martine Poux Joel Bertrand Laboratoire de GCnie Chimique,URA CNRS, Toulouse
907
6 References [ 11 Babski, V., Zhukov, M. and Yudovich, V., Mathematical Theory of Electrophoresis: Applications to Methods of Fractionation of Poly-
mers, Naukova Dumka, Kiev 1983. [21 Thormann, W., Sep. Sci. Technol. 1984,19,455-462. [31 Fife, P. C., Palusinski, 0. A. and Su, Y., Trans. Amer. Math. Soc. 1988,3I0,759-780. [41 Kohlrausch, F., Ann. Phys. (Leipzig) 1897,62,209-216. [51 Saville, D. A. and Palusinski, 0. A., AZChE J. 1986,32, 207-214. 161 Saville, D. A. and Palusinski, 0. A., AIChe J. 1986,32, 215-223. [71 Coxon, M. and Binder M., J . Chromatogr. 1974,95, 133-145. [8] Su, Y., Palusinski, 0. A. and Fife, P. C. J. Chromalogr. 1987,405, 77-85. [91 Markowich, P. A. and Ringhofer, C. A,, Math. Computation, 1983, 40, (NO. 16l), 123- 150. [ l o ] Botha, J . and Pinder, G., Fundamental Concepts in the Numerical Solutions ofDifferentialEquations, J . Wiley-Interscience, New York 1983.
Preparative free-flow isoelectric focusing: Modeling- and experiments -
Free-flow isoelectric focusing was adapted to preparative scale separations and chemical engineering methods were used to describe the main mechanisms operating in the apparatus. A mixture ofhuman serum albumin (pZ4.6) and P-lactoglobulin ( p l 5.22) was separated in pH gradients, generated with carrier ampholytes of different origin and covering the p H ranges 4-6.5,3.5-5,4-5.5 and 4.5-5.0. Best results were obtained in the p H 4-5.5 range. The experimental results have validated the results obtained with a numerical model.
1 Introduction Isoelectric focusing (IEF) is a method in which a p H gradient is developed and amphoteric molecules (generally proteins) are separated according to their isoelectric points (pl). The pls of charged species correspond to the pH for which the total charge is zero. In the presence of an electric field and a p H gradient, a protein will migrate until it reaches a p H equal to its pZ. Vesterberg’s synthesis of aminopolycarboxylic acids [ 1I, which generate p H gradients with a large buffer capacity and good conductivity under the effect of the electric field, has led to the widespread use of IEF. Electrophoretic velocity depends on both the electrophoretic mobility, which is characteristic of a protein, and the electric field. In free-flow preparative electrophoretic devices, however, the migration distance of the protein depends on the electrophoretic velocity and on the liquid velocity. Previous results from free-flow electrophoresis have aided us in perfecting our IEF apparatus. Some apparatus are operated in a recycling mode. The recycle is introduced in order to increase the residence time of the proCorrespondence: Dr. Martine Poux, Laboratoire de Genie Chimique, URA CNRS, 192 -Chemin delaloge, F-3 1078ToulouseCedex,France
Abbreviations: IEF, isoelectric focusing; p2, isoelectric point; RIEF, recycling isoelectric focusing 0VCH Verlagsgesellschaft mbH, D-6940 Weinheim, 1990
teins in the cell. Since electrophoretic velocity decreases when the protein approaches its PI,a long electrophoresis time is needed to reach a stationary state. Two geometric forms are available for the focusing cell, the parallelepiped form, as in the first apparatus, developed by Hannig [2]; and the cylindrical form, as in the apparatus proposed by Jonsson et al. [3, 41. Considerable investigations in the field of preparative IEF were performed in Bier’s laboratory, which has developed in Rotofor [51 and recycling I E F (RIEF) [6-81. Recently, Righetti et al. [91 developed adevice with anewtechnology for trapping impurities in immobilized pH gradient segments. Because of the difficulties encountered in selecting optimum running conditions, a theoretical study of the phenomena occurring in the cell has been undertaken. This numerical model makes it possible to evaluate the influence of several parameters (electric field strength, dimensions, etc.) at a lower cost than experiments. Similar investigations were performed for zone electrophoresis concerning the modeling of hydrodynamics [ 10-131. We used an identical approach to simulate the IEF process in a free-flow recycling cell. A numerical model had been presented previously and the influence of parameters such as flow rate, length and width of the cell, as well as electric field strength were studied 114, 151. In this paper, we present new parametric studies and show the validity of the model. Experimental and theoretical results of several separations of artificial protein mixtures are compared. 0173-0835/90/1I 11-0907 %3.50+.25/0
908
M. Poux and J. Bertrand
Electrophoresis 1990, 11, 907-912
2 Materials and methods
difference method with a Gauss-Seidel algorithm (for details see [10-121).
2.1 Apparatus Figure 1 shows the free-flow IEF apparatus which was the subject of our investigation [ 161, as proposed by Constans I 171. It can be considered to be a modified version of RIEF. The major differences lie in the existence of large-volume stirred vessels, the absence of membranes in the separation compartment and the cooled cell walls. For a detailed description, see [14, 17, 181.
2.2 Numerical method for process simulation Electrophoretic separation is disturbed by several phenomena, the main ones of which are considered in this study: (i) electroosmosis, created by the charge at the wall ofthe separation cell and (ii) lateral thermal gradients, induced by the Joule effect. The liouid velocity profile in the thickness of the cell is parabolic, as in laminar flow, and therefore induces a different residence time for the proteins in the separation cell. The combination of these phenomena causes the deformation of the circular entrance spot into a crescent-shaped spot. The numerical model for the simulation of the I E F process in the free-flow IEF recycle cell is divided in two parts. The first part concerns the hydrodynamics of the cell and can be treated as a classical problem in the chemical engineering methods. The model is based on the hydrodynamic equations of continuity, motion, and energy, and considers the phenomena previously described. Some hypotheses are made in order to reduce the complexity of these equations and to show dimensionless numbers such as Reynolds, Grashof and Peclet numbers. The solution method which was chosen is a finite
In the second part, the trajectory of a protein in the cell is calculated by means of the hydrodynamic velocity field obtained in the first part (which gives the three components of velocity in every point of a two-dimensional grid) and the electrophoretic velocity of the protein. The equations and the flow chart are detailed in [ 14,151. This model shows the partition of the protein in the vessels as a function of electrophoresis time. Some parameters have a direct influence on the separation of mixed proteins. In this paper, we will show what influence the number of compartments has on the separation of three proteins (for an identical width of the separation chamber): albumin (p14.60), a-lactalbumin ( ~ 1 4 . 8 8and ) P-lactoglobulin (p15.22). The properties of the separation medium are given in [ 141;the input data of the simulation program and the running conditions are presented in Table 1. 2.3 Experimental method 2.3.1 Materials The pH gradient was generated in the cell with a 1 % w/v solution of preblended carrier ampholytes Ampholine (LKB, Bromma, Sweden), pH range 4-6.5 and 3.5-5, or Servalyt (Serva, Heidelberg, FRG), pH range 4-4.5,4.5-5 and 5-5.5. Human albumin was prepared from serum and p-lactoglobulin was purchased from Sigma (St. Louis, MO). Ultrathin layer I E F was run in the PhastSystem (Pharmacia, Uppsala, Sweden), with the running conditions suggested by the manufacturer. Acetic acid, potassium hydroxide, phenylalanine and glycine were analytical grade. All solutions were degassed with ultrasound or under vacuum before use.
2.3.2 Methods The experimental study was performed with an artificial mixture of the proteins albumin and P-lactoglobulin. The injected amounts were 0.1 and 0.05 g, respectively. First, the electrode compartments were filled with the corresponding electrode buffers. Then the separation chamber and the vessels were filled with the solution of carrier ampholytes. The proteins were diluted in the liquid and injected into one of the tanks without prefocusing. The experimental data are summarized in Table 2. After running for 5 h, the fractions were
a
Table 1. Input data and running conditions for the numerical study ofthe number of compartments a)
E 2
Length (cm) Width (cm) Thickness (cm) Flow rate (rnLs-I) Volume of the tanks (mL) Electric field strength (Vm-I) Number of compartments pH range
3
4
Figure I . Preparative free-flow IEF cell. a, b, Peristaltic pumps; c, anodic vessel; d, cathodic vessel; e, anodic compartment; f, cathodic compartment; g, one compartment of the separation chamber; h, stirred tank.
Re Pe Gr Injection tank
20 20 20 9 9 9 0.2 0.2 0.2 2.375 1C2 2.375 1@* 2.375 1@' 20 20 20 5500 5500 5500 9 5 7 4-6 4-6 4-6 0.496 0.038 1.75
0.695 0.038 1.75
0.892 0.038 1.75
2
2
3
a) Re, Pe, Gr are Reynolds, Peclet and Grashofnumbers, respectively, and are defined in previous papers !14- 16I.
Preparative isoelectric focusing
Electrophoresis 1990,l I, 901-9 12
909
Table 2. Separation of the mixture albumin and P-lactoglobulin: geometric data and running conditions for the three experiments Running conditions
Characteristics of the cell
Electric field strength (V/m) 5000 Flow rate in the separation cell (mL/min) 0.8 Flow rate in the electrode compartments (mL/min) 8 20 Volume of the tanks (mL) Volume of the electrode tanks (mL) 500 Temperature (“C) 12
20 10 0.2 10
Length (cm) Width (cm) Thickness (cm) Number of tanks
Composition of the solutions for the electrodes Anodic compartment Cathodic compartment
pH Gradient
Composition of the liquid flow
Injection tank
pH 4-6.5
Ampholine 1 % pH 4-6.5
3
0.01 M Acetic acid pH 3.40
pH 3.5-5
Ampholine 1 % pH 3.5 -5
6
0.01 M Acetic acid pH 3.40
0.01 M Potassium hydroxide pH 11.60 0 . 0 1 ~Phenylalanine pH 6.40
pH 4-5.5
Servalyt 1 % pH 4-4.5 pH 4.5-5 pH 5-5.5
5
0.01 M Acetic acid pH 3.40
0.01 M Clycine pH 5.50
~~
collected from each vessel and the absorbance was measured at 280 nm. The samples were then analyzed by gel IEF.
3 Results and discussion 3.1 Parametric study
To maintain identical residence times, the flow rate for the three configurations was kept constant. As aconsequence, the axial velocity was different and the Reynolds number was changed, but this does not involve a significantmodification of 1,O
1 concentration coefficient
1 ,O
1
1 ,O
~
~
~~~
~~~~~~~~~~~
~
the hydrodynamics. The injection tank was chosen in order to inject the protein mixture at around the same pH value. When the pH gradient was fully established in the cell, it was possible to divided it into several narrow pH gradients. These pH gradients, called ApH, were developed in each compartment and became narrow when there was a large number of compartments. In consequence, two proteins which have their PIS in the ApHrangeweremixedagainat theexit OfthecelLTheeffect of increasing the number of compartments is illustrated in Fig. 2. After running for 5 h, the mixture was not completely separated, whatever the number ofcompartments. But in ace11 with 7 compartments, a large amount (75 %) of p-lactoglobulin was collected. When a cell with 9 compartments was
1 concentration coefficient
concentration coefficient
I 1
albumin
@ lactoglobulin
I
Figure 2. Distribution of albumin, a-lactalbumin and P-lactoglobulin in the vessels of a cell with 5,7 and 9 compartments after running for 5 h. The anodic side of the cell corresponds to tank I .
9 10 I ,O
Electrophoresis 1990,II, 907-912
M. Poux and J. Bertrand
1 concentration coefficient
1 ,O
-.1
1
2
3
4
1 concentration coefficient
1
5
2
3
4
5
6
7
concentration coefficient
l'O 0.8
0.6
0,4
Figure 3. Distribution of albumin, a-lactalbumin and P-lactoglobulin in the vessels of a cell with 5 , 7 and 9 compartments after running for 6 h 30 min. The anodic side of the cell corresponds to tank 1.
tank number 1 2 3 4 5 6 7 8 9
used, all albumin, 80 % of the P-lactoglobulin and 40 % of the a-lactalbumin were purified. When the running time was increased (6 h 30 min) a complete separation was achieved (Fig. 3). In the other cases, the operating conditions did not allow for a complete separation of the three proteins.
PH
When the protein was near it PI,its electrophoretic velocity decreased. This and the electroosmosis phenomenon were limiting factors which tended to spread the protein to several vessels. In a cell with 9 compartments, a-lactalbumin was collected in two tanks (as illustrated in Fig. 3). Therefore, a long running time is needed to achieve a stationary state and total protein focusing.
3.2 Experimental results A mixture of albumin and P-lactoglobulin was separated in the free-flow IEF cell in three pH gradients: pH range 4-6.5, 3.5-5 and 4-5.5. Figures 4-6 presents the IEF gels, the absorbance of the fractions (which were collected in the tanks after running for 5 h) and the profiles of the pH gradients. A complete separation of the two proteins was not achieved with the pH 4-6.5 range. Absorbance measurements show a great deal of protein in tanks 3 and 4, with traces in tanks 2 and 5. The proteins were identified by IEF gel analysis: tank 3 and tank 4 became enriched by albumin and P-lactoglobulin, respectively. The pH ofthe solution which corresponded to the pls of these proteins was located at the anodic side of the cell. The pH gradient profile, developed in the separation chamber, was not linear and represented a high increase at this side. In this region, the separation is more difficult because ofthe ApH value. ofthe proteins were When a pH 3.5-5 range was used, the PIS located at the cathodic side, where a concentration gradient
1
2 3 4
0
5
6
7
8
910
0 0
pH =4
+
albumin Blactoglobulin -b
t
4
pH =6,5
Figurel. Separationofalbumin and P-lactoglobulininthe free-flowIEF cell after running for 5 h in a p H gradient of4-6.5. (A) Absorbance (280 nm)of the samples collected in the tanks and pH gradient. The pH values are measured in the tanks. (B) Analysis of the samples collected in the tanks by ultrathin-layer gel IEF, pH gradient 4-6.5. (1) Initial mixture, (2) tank 1; (3) tank 2; (4) tank 3, (5) tank 4, (6) tank 5 .
Electrophoresis 1990,11, 907-912
Preparative isbelectric focusing
9 11
PH
D.0 5,OO
5.00
4,OO
4.00
tank number
tank number
1 2 3 4 5 6 7 8 9 1 0
0
+
albumin B-lactoglobulin -b
albumin -& 8-lactoglobulin pH =6,5 1
2
3
4
5
6
7
8
pH =6,5
0 1
2
3
4
5
6
7
0
Figure 5.Separation of albumin and P-lactoglobulinin the free-flow IEF cell after running for 5 h in a p H gradientof 3.5-5.(A)Absorbance(280nm)of the samples collected in the tanks and pH gradient. The pH values are measured in the tanks. (B) Analysis of the samples collected in the tanks by ultrathin-layer gel IEF, p H gradient 4-6.5. (1) Initial mixture, (2) tank 4; (3) tank 5, (4)tank 6, (5) tank 7, (6) tank 8, (7) tank 9, ( 8 ) tank 10.
Figure 6. Separation of albumin and P-lactoglobulin in the free-flow IEF cell after running for 5 h in a p H gradientof4-5.5.(A)Absorbance(280nm)of the samples collected in the tanks and pH gradient. The p H values are measuredin the tanks. (B) Analysis ofthe samples collected in the tanks by ultrathin-layergelIEF,pHgradient4-6.5.(1)Tank 3,(2)tank4,(3)tank5, (4)tank 6, (5) tank 7, (6) tank 8, (7) initial mixture.
was created because of the presence of the cellophane membrane. The proteins were spread over several tanks and required a long focusing time. Consequently, the proteins (after running for 5 h) were distributed in the last five tanks. This pH gradient, which appeared to be more linear, and the running conditions were not optimal for the separation of albumin and P-lactoglobulin.
the pH values, recorded every 15 min in all compartment during the running time, was considered to simulate the experiments. The histograms in Fig. 7 represent the dimensionless concentration of the two proteins, after running for 5h, with respect to the amount of protein in the vessels. Theexperimental distribution of the proteins in the tanks was similar to a Gaussian curve, trailing towards the cathodic side. This trailing may be attributed to electroosmosis [20]. It is a phenomenon which was also observed by the computation, although less pronounced. Numerical results for the separation in the pH ranges of 4-6.5 and 4-5.5 are in good agreement with the experiments. In the other experiment, the compartment in which the proteins focused was displaced towards the cathodic side: this effect predominated when albumin was present. A report is pending on this observation, which can be attributed to thecellophane membrane and to boundary effects.
It may be possible to achieve a separation of albumin and P-lactoglobulin in the central part of the cell, far from the electrode compartments, with a pH 4-5.5 range. Here, the proteins were concentrated in tanks 4 to 7. The absorbance level and the IEF gel showed that tanks 5 and 6 were enriched by albumin. Some traces of this protein remained in tank 4, while P-lactoglobulin was concentrated in tank 7 without any trace of albumin having been detected in the IEF gels. A great amount of P-lactoglobulin was also contained in tank 6 and some traces in tanks 5 and 8. Although the separation was incomplete, this p H gradient seemed to be the best ofthe three p H ranges studied.
3.3 Numerical results compared with experiments The electrophoretic mobility of the proteins as a function of the pH were calculated from experimental data given in the literature [ 191. The variation of the pH gradient according to
4 Concluding remarks In this paper, we have shown examples of parametric studies with the numerical model, validated by several experiments. Numerical analyses are limited because first the following data is necessary: (i) the equations of the electrophoretic mobilities of the proteins have to be calculated in a liquid solution with a pH gradient, (ii) the pH values need to also be
9 12
M. Poux and J. Bertrand
Eiectrophoresis 1990, I I , 907-9 12
- concenaationcoefficient "I"
0,5 0,4
0,3
02
tank number
0.0 1
0,6
1
2
3
4
5
1
6 7 8 9 I0
2
4
3
5
6
7
8 9 10
pH range 3.5-5
pH range 4-6.5
concenaation coefficient
0,5 0.4
albumin El B-lactoglobulin
0,3
I
1
0.2 0, I
tank number
0 0
1 2 3 4 5 6 7 8 9 1 0
pH range 4-5.5
measured in the cell and not only in the vessels, and (iii) the value of the electroosmotic velocity at the walls has to be known. Future investigations will focus on refinements of the model. Some limits will always exist, however, due to the problem with carrier ampholytes (e.g. uneven buffering capacity and conductivity, unknown chemical environment and binding with proteins). The following extensions can be included to improve the agreement between the numerical and experimental results: (i) axial thermal gradients, (ii) internal geometry of the compartments at the top andthe bottom ofthe separation cell, and (iii) variation of the electric conductivity with the pH gradient. This will create an improved numerical model, able to simulate separations of biological products. It will be possible to predict the optimal running conditions for the separation of mixed proteins and, therefore, to limit the number of experiments. Received June 5, 1990
5 References [ 11 Vesterberg, O., Acta Chem. Scnnd. 1969,23,2653-2666. 121 Hannig, K., Wirth, H., Schindler, R. K. and Spiegel, K., Hoppe Seyler's Z. Physiol. Chem. 1977,358, 753-763. 131 Jonsson, M. and Rilbe, H., Electrophoresis 1980, 1, 3-14. [41 Jonsson, M. and Fredricksson, S., Electrophoresis 198 1,2,193-204. [51 Egen, N. B., Thormann, W., Twitty, G. E. and Bier, M., in: Hirai H. (Ed.), E/ectrophoresis'83, Walter de Guyter, Berlin, 1984, pp. 547-550.
Figure 7.Simulation of the separation ofthe mixture albumin and P-lactoglobulin in the three pH ranges. 161 Bier, M. and Egen, N. B., in: Haglund, H., Westerfeld, J. G. and Ball,
J.T.(Eds.),ElectroSocus '78,Elsevier, Amsterdam 1979,pp. 35-48. I7 I Bier, M., Egen, N. B., Allgyer, T. T., Twitty, G. E. and Mosher, R. A., in: Gross, E. and Meienhofer, J . (Eds.), Peptides: Structure and Biologics/ Function Pierce Chemical Illinois 1979, pp. 79-89. [8l Bier, M., Egen, N. B., Twitty, G. E., Mosher, R. A., and Thormann, W., in: King, C. J. and Navratil, J. D. (Eds.), Chemica/Separations Litarvan Literature, Denver 1986, pp. 133-151. 19) Righetti, P. G., Barzachi, B., Luzzana, M., Manfredi, G. and Faupel, M., J . Biochem. Biophys. Methods 1987,15, 189-198. 101 Biscans, B., Alinat, P., Bertrand, J . and Sanchez, V., Electrophoresis 1988,9,84-89. I l l Biscans, B. and Bertrand, J., Chem. Eng. Res. Des. 1987, 65, 224-230. 12) Biscans, B. andBertrand,J. Comp. Chem.Eng. 1988,12,177-182. 131 Biscans, B., Bertrand,J. andSanchez, V., Can. J . Chem. Eng. 1986, 64,726-733. [ I41 Poux, M., Biscans, B. and Bertrand,J, Trans. Inst. Chem.Eng. 1990, 68,278-286. I 151 Poux, M., Biscans, B. and Bertrand, J.,in: Stork, A. and Grevillot, G., (Eds.), Rkcents Progris en Gknie des Procidks Paris, Lavoisier, Tec. DOC.1987,2, pp. 146-151. 161 Poux, M., These de Doctoraa, INP Toulouse, France, 1989. [ 171 Lopez, A., Clerc, A., Poux, M. and Constans, J. Revue Inst. Pasteur Lyon 1987,20, 1-2, 15-24. 1181 Poux, M., Biscans, B. and Bertrand, J., in:,Schafer-Nielsen, (Ed.), Electrophoresis '88, VCH Verlagsgesellschaft, Weinheim 1988, pp. 181-186. 1191 Casademont,E. andSanchez,V.,J. Chim.Phys. 1981,78,843-849. [201 Poux, M. and Bertrand, J., in: Bertrand, J., Gourdon, C., and Riba, J . P., (Eds.), RPcents Progris en Ge'nie des Proce'dis Paris, Lavoisier, Tec. Doc. 1989,3, pp. 381-386.
Preparative isoelectric focusing
erature only gave satisfactory results for a limited range of parameters. In contrast, the method reported here has no restrictions of this kind. The computational procedure was constructed on the basis of our previous theoretical analysis. The convergence of iterations is theoretically assured and the only restriction to accuracy is the cumulation of round-off errors. The method provides a basis for estimating the errors due to theelectroneutrality approximation. For the threeexamples considered here, these errors d o not exceed 0.02 %, with larger errors corresponding to the largest value of E=O.O 1.Therefore, we can state that the electroneutrality approximation can indeed be used in those three cases. Received June 5, 1990
Martine Poux Joel Bertrand Laboratoire de GCnie Chimique,URA CNRS, Toulouse
907
6 References [ 11 Babski, V., Zhukov, M. and Yudovich, V., Mathematical Theory of Electrophoresis: Applications to Methods of Fractionation of Poly-
mers, Naukova Dumka, Kiev 1983. [21 Thormann, W., Sep. Sci. Technol. 1984,19,455-462. [31 Fife, P. C., Palusinski, 0. A. and Su, Y., Trans. Amer. Math. Soc. 1988,3I0,759-780. [41 Kohlrausch, F., Ann. Phys. (Leipzig) 1897,62,209-216. [51 Saville, D. A. and Palusinski, 0. A., AZChE J. 1986,32, 207-214. 161 Saville, D. A. and Palusinski, 0. A., AIChe J. 1986,32, 215-223. [71 Coxon, M. and Binder M., J . Chromatogr. 1974,95, 133-145. [8] Su, Y., Palusinski, 0. A. and Fife, P. C. J. Chromalogr. 1987,405, 77-85. [91 Markowich, P. A. and Ringhofer, C. A,, Math. Computation, 1983, 40, (NO. 16l), 123- 150. [ l o ] Botha, J . and Pinder, G., Fundamental Concepts in the Numerical Solutions ofDifferentialEquations, J . Wiley-Interscience, New York 1983.
Preparative free-flow isoelectric focusing: Modeling- and experiments -
Free-flow isoelectric focusing was adapted to preparative scale separations and chemical engineering methods were used to describe the main mechanisms operating in the apparatus. A mixture ofhuman serum albumin (pZ4.6) and P-lactoglobulin ( p l 5.22) was separated in pH gradients, generated with carrier ampholytes of different origin and covering the p H ranges 4-6.5,3.5-5,4-5.5 and 4.5-5.0. Best results were obtained in the p H 4-5.5 range. The experimental results have validated the results obtained with a numerical model.
1 Introduction Isoelectric focusing (IEF) is a method in which a p H gradient is developed and amphoteric molecules (generally proteins) are separated according to their isoelectric points (pl). The pls of charged species correspond to the pH for which the total charge is zero. In the presence of an electric field and a p H gradient, a protein will migrate until it reaches a p H equal to its pZ. Vesterberg’s synthesis of aminopolycarboxylic acids [ 1I, which generate p H gradients with a large buffer capacity and good conductivity under the effect of the electric field, has led to the widespread use of IEF. Electrophoretic velocity depends on both the electrophoretic mobility, which is characteristic of a protein, and the electric field. In free-flow preparative electrophoretic devices, however, the migration distance of the protein depends on the electrophoretic velocity and on the liquid velocity. Previous results from free-flow electrophoresis have aided us in perfecting our IEF apparatus. Some apparatus are operated in a recycling mode. The recycle is introduced in order to increase the residence time of the proCorrespondence: Dr. Martine Poux, Laboratoire de Genie Chimique, URA CNRS, 192 -Chemin delaloge, F-3 1078ToulouseCedex,France
Abbreviations: IEF, isoelectric focusing; p2, isoelectric point; RIEF, recycling isoelectric focusing 0VCH Verlagsgesellschaft mbH, D-6940 Weinheim, 1990
teins in the cell. Since electrophoretic velocity decreases when the protein approaches its PI,a long electrophoresis time is needed to reach a stationary state. Two geometric forms are available for the focusing cell, the parallelepiped form, as in the first apparatus, developed by Hannig [2]; and the cylindrical form, as in the apparatus proposed by Jonsson et al. [3, 41. Considerable investigations in the field of preparative IEF were performed in Bier’s laboratory, which has developed in Rotofor [51 and recycling I E F (RIEF) [6-81. Recently, Righetti et al. [91 developed adevice with anewtechnology for trapping impurities in immobilized pH gradient segments. Because of the difficulties encountered in selecting optimum running conditions, a theoretical study of the phenomena occurring in the cell has been undertaken. This numerical model makes it possible to evaluate the influence of several parameters (electric field strength, dimensions, etc.) at a lower cost than experiments. Similar investigations were performed for zone electrophoresis concerning the modeling of hydrodynamics [ 10-131. We used an identical approach to simulate the IEF process in a free-flow recycling cell. A numerical model had been presented previously and the influence of parameters such as flow rate, length and width of the cell, as well as electric field strength were studied 114, 151. In this paper, we present new parametric studies and show the validity of the model. Experimental and theoretical results of several separations of artificial protein mixtures are compared. 0173-0835/90/1I 11-0907 %3.50+.25/0
908
M. Poux and J. Bertrand
Electrophoresis 1990, 11, 907-912
2 Materials and methods
difference method with a Gauss-Seidel algorithm (for details see [10-121).
2.1 Apparatus Figure 1 shows the free-flow IEF apparatus which was the subject of our investigation [ 161, as proposed by Constans I 171. It can be considered to be a modified version of RIEF. The major differences lie in the existence of large-volume stirred vessels, the absence of membranes in the separation compartment and the cooled cell walls. For a detailed description, see [14, 17, 181.
2.2 Numerical method for process simulation Electrophoretic separation is disturbed by several phenomena, the main ones of which are considered in this study: (i) electroosmosis, created by the charge at the wall ofthe separation cell and (ii) lateral thermal gradients, induced by the Joule effect. The liouid velocity profile in the thickness of the cell is parabolic, as in laminar flow, and therefore induces a different residence time for the proteins in the separation cell. The combination of these phenomena causes the deformation of the circular entrance spot into a crescent-shaped spot. The numerical model for the simulation of the I E F process in the free-flow IEF recycle cell is divided in two parts. The first part concerns the hydrodynamics of the cell and can be treated as a classical problem in the chemical engineering methods. The model is based on the hydrodynamic equations of continuity, motion, and energy, and considers the phenomena previously described. Some hypotheses are made in order to reduce the complexity of these equations and to show dimensionless numbers such as Reynolds, Grashof and Peclet numbers. The solution method which was chosen is a finite
In the second part, the trajectory of a protein in the cell is calculated by means of the hydrodynamic velocity field obtained in the first part (which gives the three components of velocity in every point of a two-dimensional grid) and the electrophoretic velocity of the protein. The equations and the flow chart are detailed in [ 14,151. This model shows the partition of the protein in the vessels as a function of electrophoresis time. Some parameters have a direct influence on the separation of mixed proteins. In this paper, we will show what influence the number of compartments has on the separation of three proteins (for an identical width of the separation chamber): albumin (p14.60), a-lactalbumin ( ~ 1 4 . 8 8and ) P-lactoglobulin (p15.22). The properties of the separation medium are given in [ 141;the input data of the simulation program and the running conditions are presented in Table 1. 2.3 Experimental method 2.3.1 Materials The pH gradient was generated in the cell with a 1 % w/v solution of preblended carrier ampholytes Ampholine (LKB, Bromma, Sweden), pH range 4-6.5 and 3.5-5, or Servalyt (Serva, Heidelberg, FRG), pH range 4-4.5,4.5-5 and 5-5.5. Human albumin was prepared from serum and p-lactoglobulin was purchased from Sigma (St. Louis, MO). Ultrathin layer I E F was run in the PhastSystem (Pharmacia, Uppsala, Sweden), with the running conditions suggested by the manufacturer. Acetic acid, potassium hydroxide, phenylalanine and glycine were analytical grade. All solutions were degassed with ultrasound or under vacuum before use.
2.3.2 Methods The experimental study was performed with an artificial mixture of the proteins albumin and P-lactoglobulin. The injected amounts were 0.1 and 0.05 g, respectively. First, the electrode compartments were filled with the corresponding electrode buffers. Then the separation chamber and the vessels were filled with the solution of carrier ampholytes. The proteins were diluted in the liquid and injected into one of the tanks without prefocusing. The experimental data are summarized in Table 2. After running for 5 h, the fractions were
a
Table 1. Input data and running conditions for the numerical study ofthe number of compartments a)
E 2
Length (cm) Width (cm) Thickness (cm) Flow rate (rnLs-I) Volume of the tanks (mL) Electric field strength (Vm-I) Number of compartments pH range
3
4
Figure I . Preparative free-flow IEF cell. a, b, Peristaltic pumps; c, anodic vessel; d, cathodic vessel; e, anodic compartment; f, cathodic compartment; g, one compartment of the separation chamber; h, stirred tank.
Re Pe Gr Injection tank
20 20 20 9 9 9 0.2 0.2 0.2 2.375 1C2 2.375 1@* 2.375 1@' 20 20 20 5500 5500 5500 9 5 7 4-6 4-6 4-6 0.496 0.038 1.75
0.695 0.038 1.75
0.892 0.038 1.75
2
2
3
a) Re, Pe, Gr are Reynolds, Peclet and Grashofnumbers, respectively, and are defined in previous papers !14- 16I.
Preparative isoelectric focusing
Electrophoresis 1990,l I, 901-9 12
909
Table 2. Separation of the mixture albumin and P-lactoglobulin: geometric data and running conditions for the three experiments Running conditions
Characteristics of the cell
Electric field strength (V/m) 5000 Flow rate in the separation cell (mL/min) 0.8 Flow rate in the electrode compartments (mL/min) 8 20 Volume of the tanks (mL) Volume of the electrode tanks (mL) 500 Temperature (“C) 12
20 10 0.2 10
Length (cm) Width (cm) Thickness (cm) Number of tanks
Composition of the solutions for the electrodes Anodic compartment Cathodic compartment
pH Gradient
Composition of the liquid flow
Injection tank
pH 4-6.5
Ampholine 1 % pH 4-6.5
3
0.01 M Acetic acid pH 3.40
pH 3.5-5
Ampholine 1 % pH 3.5 -5
6
0.01 M Acetic acid pH 3.40
0.01 M Potassium hydroxide pH 11.60 0 . 0 1 ~Phenylalanine pH 6.40
pH 4-5.5
Servalyt 1 % pH 4-4.5 pH 4.5-5 pH 5-5.5
5
0.01 M Acetic acid pH 3.40
0.01 M Clycine pH 5.50
~~
collected from each vessel and the absorbance was measured at 280 nm. The samples were then analyzed by gel IEF.
3 Results and discussion 3.1 Parametric study
To maintain identical residence times, the flow rate for the three configurations was kept constant. As aconsequence, the axial velocity was different and the Reynolds number was changed, but this does not involve a significantmodification of 1,O
1 concentration coefficient
1 ,O
1
1 ,O
~
~
~~~
~~~~~~~~~~~
~
the hydrodynamics. The injection tank was chosen in order to inject the protein mixture at around the same pH value. When the pH gradient was fully established in the cell, it was possible to divided it into several narrow pH gradients. These pH gradients, called ApH, were developed in each compartment and became narrow when there was a large number of compartments. In consequence, two proteins which have their PIS in the ApHrangeweremixedagainat theexit OfthecelLTheeffect of increasing the number of compartments is illustrated in Fig. 2. After running for 5 h, the mixture was not completely separated, whatever the number ofcompartments. But in ace11 with 7 compartments, a large amount (75 %) of p-lactoglobulin was collected. When a cell with 9 compartments was
1 concentration coefficient
concentration coefficient
I 1
albumin
@ lactoglobulin
I
Figure 2. Distribution of albumin, a-lactalbumin and P-lactoglobulin in the vessels of a cell with 5,7 and 9 compartments after running for 5 h. The anodic side of the cell corresponds to tank I .
9 10 I ,O
Electrophoresis 1990,II, 907-912
M. Poux and J. Bertrand
1 concentration coefficient
1 ,O
-.1
1
2
3
4
1 concentration coefficient
1
5
2
3
4
5
6
7
concentration coefficient
l'O 0.8
0.6
0,4
Figure 3. Distribution of albumin, a-lactalbumin and P-lactoglobulin in the vessels of a cell with 5 , 7 and 9 compartments after running for 6 h 30 min. The anodic side of the cell corresponds to tank 1.
tank number 1 2 3 4 5 6 7 8 9
used, all albumin, 80 % of the P-lactoglobulin and 40 % of the a-lactalbumin were purified. When the running time was increased (6 h 30 min) a complete separation was achieved (Fig. 3). In the other cases, the operating conditions did not allow for a complete separation of the three proteins.
PH
When the protein was near it PI,its electrophoretic velocity decreased. This and the electroosmosis phenomenon were limiting factors which tended to spread the protein to several vessels. In a cell with 9 compartments, a-lactalbumin was collected in two tanks (as illustrated in Fig. 3). Therefore, a long running time is needed to achieve a stationary state and total protein focusing.
3.2 Experimental results A mixture of albumin and P-lactoglobulin was separated in the free-flow IEF cell in three pH gradients: pH range 4-6.5, 3.5-5 and 4-5.5. Figures 4-6 presents the IEF gels, the absorbance of the fractions (which were collected in the tanks after running for 5 h) and the profiles of the pH gradients. A complete separation of the two proteins was not achieved with the pH 4-6.5 range. Absorbance measurements show a great deal of protein in tanks 3 and 4, with traces in tanks 2 and 5. The proteins were identified by IEF gel analysis: tank 3 and tank 4 became enriched by albumin and P-lactoglobulin, respectively. The pH ofthe solution which corresponded to the pls of these proteins was located at the anodic side of the cell. The pH gradient profile, developed in the separation chamber, was not linear and represented a high increase at this side. In this region, the separation is more difficult because ofthe ApH value. ofthe proteins were When a pH 3.5-5 range was used, the PIS located at the cathodic side, where a concentration gradient
1
2 3 4
0
5
6
7
8
910
0 0
pH =4
+
albumin Blactoglobulin -b
t
4
pH =6,5
Figurel. Separationofalbumin and P-lactoglobulininthe free-flowIEF cell after running for 5 h in a p H gradient of4-6.5. (A) Absorbance (280 nm)of the samples collected in the tanks and pH gradient. The pH values are measured in the tanks. (B) Analysis of the samples collected in the tanks by ultrathin-layer gel IEF, pH gradient 4-6.5. (1) Initial mixture, (2) tank 1; (3) tank 2; (4) tank 3, (5) tank 4, (6) tank 5 .
Electrophoresis 1990,11, 907-912
Preparative isbelectric focusing
9 11
PH
D.0 5,OO
5.00
4,OO
4.00
tank number
tank number
1 2 3 4 5 6 7 8 9 1 0
0
+
albumin B-lactoglobulin -b
albumin -& 8-lactoglobulin pH =6,5 1
2
3
4
5
6
7
8
pH =6,5
0 1
2
3
4
5
6
7
0
Figure 5.Separation of albumin and P-lactoglobulinin the free-flow IEF cell after running for 5 h in a p H gradientof 3.5-5.(A)Absorbance(280nm)of the samples collected in the tanks and pH gradient. The pH values are measured in the tanks. (B) Analysis of the samples collected in the tanks by ultrathin-layer gel IEF, p H gradient 4-6.5. (1) Initial mixture, (2) tank 4; (3) tank 5, (4)tank 6, (5) tank 7, (6) tank 8, (7) tank 9, ( 8 ) tank 10.
Figure 6. Separation of albumin and P-lactoglobulin in the free-flow IEF cell after running for 5 h in a p H gradientof4-5.5.(A)Absorbance(280nm)of the samples collected in the tanks and pH gradient. The p H values are measuredin the tanks. (B) Analysis ofthe samples collected in the tanks by ultrathin-layergelIEF,pHgradient4-6.5.(1)Tank 3,(2)tank4,(3)tank5, (4)tank 6, (5) tank 7, (6) tank 8, (7) initial mixture.
was created because of the presence of the cellophane membrane. The proteins were spread over several tanks and required a long focusing time. Consequently, the proteins (after running for 5 h) were distributed in the last five tanks. This pH gradient, which appeared to be more linear, and the running conditions were not optimal for the separation of albumin and P-lactoglobulin.
the pH values, recorded every 15 min in all compartment during the running time, was considered to simulate the experiments. The histograms in Fig. 7 represent the dimensionless concentration of the two proteins, after running for 5h, with respect to the amount of protein in the vessels. Theexperimental distribution of the proteins in the tanks was similar to a Gaussian curve, trailing towards the cathodic side. This trailing may be attributed to electroosmosis [20]. It is a phenomenon which was also observed by the computation, although less pronounced. Numerical results for the separation in the pH ranges of 4-6.5 and 4-5.5 are in good agreement with the experiments. In the other experiment, the compartment in which the proteins focused was displaced towards the cathodic side: this effect predominated when albumin was present. A report is pending on this observation, which can be attributed to thecellophane membrane and to boundary effects.
It may be possible to achieve a separation of albumin and P-lactoglobulin in the central part of the cell, far from the electrode compartments, with a pH 4-5.5 range. Here, the proteins were concentrated in tanks 4 to 7. The absorbance level and the IEF gel showed that tanks 5 and 6 were enriched by albumin. Some traces of this protein remained in tank 4, while P-lactoglobulin was concentrated in tank 7 without any trace of albumin having been detected in the IEF gels. A great amount of P-lactoglobulin was also contained in tank 6 and some traces in tanks 5 and 8. Although the separation was incomplete, this p H gradient seemed to be the best ofthe three p H ranges studied.
3.3 Numerical results compared with experiments The electrophoretic mobility of the proteins as a function of the pH were calculated from experimental data given in the literature [ 191. The variation of the pH gradient according to
4 Concluding remarks In this paper, we have shown examples of parametric studies with the numerical model, validated by several experiments. Numerical analyses are limited because first the following data is necessary: (i) the equations of the electrophoretic mobilities of the proteins have to be calculated in a liquid solution with a pH gradient, (ii) the pH values need to also be
9 12
M. Poux and J. Bertrand
Eiectrophoresis 1990, I I , 907-9 12
- concenaationcoefficient "I"
0,5 0,4
0,3
02
tank number
0.0 1
0,6
1
2
3
4
5
1
6 7 8 9 I0
2
4
3
5
6
7
8 9 10
pH range 3.5-5
pH range 4-6.5
concenaation coefficient
0,5 0.4
albumin El B-lactoglobulin
0,3
I
1
0.2 0, I
tank number
0 0
1 2 3 4 5 6 7 8 9 1 0
pH range 4-5.5
measured in the cell and not only in the vessels, and (iii) the value of the electroosmotic velocity at the walls has to be known. Future investigations will focus on refinements of the model. Some limits will always exist, however, due to the problem with carrier ampholytes (e.g. uneven buffering capacity and conductivity, unknown chemical environment and binding with proteins). The following extensions can be included to improve the agreement between the numerical and experimental results: (i) axial thermal gradients, (ii) internal geometry of the compartments at the top andthe bottom ofthe separation cell, and (iii) variation of the electric conductivity with the pH gradient. This will create an improved numerical model, able to simulate separations of biological products. It will be possible to predict the optimal running conditions for the separation of mixed proteins and, therefore, to limit the number of experiments. Received June 5, 1990
5 References [ 11 Vesterberg, O., Acta Chem. Scnnd. 1969,23,2653-2666. 121 Hannig, K., Wirth, H., Schindler, R. K. and Spiegel, K., Hoppe Seyler's Z. Physiol. Chem. 1977,358, 753-763. 131 Jonsson, M. and Rilbe, H., Electrophoresis 1980, 1, 3-14. [41 Jonsson, M. and Fredricksson, S., Electrophoresis 198 1,2,193-204. [51 Egen, N. B., Thormann, W., Twitty, G. E. and Bier, M., in: Hirai H. (Ed.), E/ectrophoresis'83, Walter de Guyter, Berlin, 1984, pp. 547-550.
Figure 7.Simulation of the separation ofthe mixture albumin and P-lactoglobulin in the three pH ranges. 161 Bier, M. and Egen, N. B., in: Haglund, H., Westerfeld, J. G. and Ball,
J.T.(Eds.),ElectroSocus '78,Elsevier, Amsterdam 1979,pp. 35-48. I7 I Bier, M., Egen, N. B., Allgyer, T. T., Twitty, G. E. and Mosher, R. A., in: Gross, E. and Meienhofer, J . (Eds.), Peptides: Structure and Biologics/ Function Pierce Chemical Illinois 1979, pp. 79-89. [8l Bier, M., Egen, N. B., Twitty, G. E., Mosher, R. A., and Thormann, W., in: King, C. J. and Navratil, J. D. (Eds.), Chemica/Separations Litarvan Literature, Denver 1986, pp. 133-151. 19) Righetti, P. G., Barzachi, B., Luzzana, M., Manfredi, G. and Faupel, M., J . Biochem. Biophys. Methods 1987,15, 189-198. 101 Biscans, B., Alinat, P., Bertrand, J . and Sanchez, V., Electrophoresis 1988,9,84-89. I l l Biscans, B. and Bertrand, J., Chem. Eng. Res. Des. 1987, 65, 224-230. 12) Biscans, B. andBertrand,J. Comp. Chem.Eng. 1988,12,177-182. 131 Biscans, B., Bertrand,J. andSanchez, V., Can. J . Chem. Eng. 1986, 64,726-733. [ I41 Poux, M., Biscans, B. and Bertrand,J, Trans. Inst. Chem.Eng. 1990, 68,278-286. I 151 Poux, M., Biscans, B. and Bertrand, J.,in: Stork, A. and Grevillot, G., (Eds.), Rkcents Progris en Gknie des Procidks Paris, Lavoisier, Tec. DOC.1987,2, pp. 146-151. 161 Poux, M., These de Doctoraa, INP Toulouse, France, 1989. [ 171 Lopez, A., Clerc, A., Poux, M. and Constans, J. Revue Inst. Pasteur Lyon 1987,20, 1-2, 15-24. 1181 Poux, M., Biscans, B. and Bertrand, J., in:,Schafer-Nielsen, (Ed.), Electrophoresis '88, VCH Verlagsgesellschaft, Weinheim 1988, pp. 181-186. 1191 Casademont,E. andSanchez,V.,J. Chim.Phys. 1981,78,843-849. [201 Poux, M. and Bertrand, J., in: Bertrand, J., Gourdon, C., and Riba, J . P., (Eds.), RPcents Progris en Ge'nie des Proce'dis Paris, Lavoisier, Tec. Doc. 1989,3, pp. 381-386.
