Ind. Eng. Chem. Fundam. 1081, 20, 171-174
a1 = 0 a2 =
yo3 4Y,2 + Kc/3
(A.7a)
R = radial coordinate, dimensionless
(A.7b)
;P,
so that
where yo is given by the solution of the equation yo
KC +In
YO
171
(t)
=0
Equations A.8 and A.9 are used to start the numerical solution. Nomenclature a = filter element (granule) radius, m C = Cunningham correction factor D = diffusion coefficient, m2/s tg= unit vector in the direction of the gravitational force e, = unit vector in the radial direction E = single collector (sphere) efficiency = single collector (sphere) efficiency due to electrical effecta F, = electrical force, N Ga = ga/Uo2= Galileo number, dimensionless g = acceleration of gravity, m/s2 KO,K1,K2,K3 = constants defined by eq 24,25,26, and 27, respectively K, = electric force constant, dimensionless mp = mass of dust particle, kg Pe = aUo/D = Peclet number, dimensionless Pee, = electrical Peclet number, P e u y , , dimensionless qn q = electrical charge on collector and particle, respectively, C L e
Qc, Qp = electrical charge density on collector and particle, respectively, pC/m2
r = radial coordinate, m = aerosol (dust particle) radius, pm or m = r$a = interception parameter S t = 2 ppU,yor,2{9pa = Stokes number T = dimension ess time X = position vector, dimensionless XL= upstream opening of limiting trajectory, dimensionless zi = fluid velocity vector, dimensionless zi, = electrical velocity vector, dimensionless u = settling velocity, dimensionless do= superficial fluid velocity, m/s y = coordinate defined by R - 1, dimensionless y o = location of nodal point, dimensionless Greek Letters t
= granular bed porosity
ef = fluid dielectric constant, (pCl2/N m2 B = polar coordinate p
= fluid viscosity kg/me
Literature Cited Balusubramanian, M.: Melsen, A.; Mathur, K. B. Can. J . Chem. €ng. 1978, 56, 298. Figueroa, A. R.: Llcht, W. A I C M Symp. Ser. No. 175 1978, 74, 17. Gutfinger, C.; Tardos, G. I. Atmos. fnvkon. 1979, 13(0), 853. Kraemer, H. F.; Johnstone, H. F. Ind. Eng. Chem. 1055, 47, 2470; 1958, 48, 812. Neale, H. N.; Nader, W. K. AIChE J. 1074, 20, 530. Nielsen, K. A.; Hill, J. C. Ind. Eng. Chem. Fundam. 1978, 75, 149, 157. Tardos, 0. I.; Pfeffer, R. "Roceedlngs, Second World Flltratlon Congress", London, 1979, 239. Tardos, G. I.; Gutfinger, C.; Pfeffer, R. Ind. €ng. Chem. Fundem. 1079, 78, 433.
Department of Chemical Engineering The City College of The City University ofNew York New York, New York 10031
Robert Pfeffer* G. I. Tardos L. M. Pismen
Received for review March 17, 1980 Accepted February 9,1981
Parametric Pumping with pH and Ionic Strength: Enzyme Purification Purification of alkaline phosphatase was experimentally investigated by semicontinuous parametric pumping. The parapumping involves reciprocating flow of the enzyme mixture to be purified through a bed of ion exchanger and, simultaneously,synchronous cyclic variation of the pH and ionic strength. The change of pH and ionlc strength displaces the interphase equilibrium and, in combination with the reciprocating flow, causes preferential movement of the sorbable components of the mixture toward one end of the bed, leading to a buildup of the separation from cycle to cycle. It is shown that the parametric pumping c a n yield a larger enzyme activity recovered with high purification factors than the conventional cycling-zone adsorption process. Introduction Parametric pumping represents a new development in separation science. It has attracted considerable attention, both because of its novelty and because it permits continuous operation in small equipment with very high Separation factors. The basic principle of parametic pumping is to utilize the coupling of periodic changes in some intensive variables (such as temperature, pressure, pH, ionic strength, or electric field) and periodic changes in flow direction to separate the components of a fluid which flow past a solid adsorbent. Techniques commonly used in the separation of fluid mixtures, including adsorption, extraction, affmity chromatography, and ion-exchange chromatography, might be adapted to parametric pumping. The adaptation could be made in principle in those situations in which a re0196-4313/81/1020-0171$01.25/0
versible differential shift in the distribution of components between a mobile and an immobile phase could conveniently and practically be brought about by variation of an intensible variable. Applications of parametric pumping involving the separation of valuable materials such as proteins may be very attractive and profitable to investigate. Shaffer and Hamrin (1975) combined affinity chromatography and parametric pumping to reduce trypsin concentration in an aqueous solution. Their results indicate that parametric pumping is a useful technique for enzyme separation. Recently, Chen et al. (1977,1979)have applied parametric pumping and ion-exchange chromatography to the separation of hemoglobin and albumin. It has been shown that under certain conditions the parapump has the capacity for removal of protein components from one product 0 1981 American Chemical Society
172
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
-
PH
I
e
0
7.4 0.6
3
A A
4.0 0.1 4 0 0.2
NAOH SOUTIO IN
k.!
IS
2 4
g,
FEED
0: I Cc/rnin EXP
7.4 0 I
@CIRCULATION @PUMPING BOTTOM BUFFER @ UPFLOW
I
I
@CIRCULATION
I
TOP
--E
BOTTOM PRODUCT
:,minules
Figure 1. Effect of buffer pH and ionic strength on adsorption.
fraction and large enrichment in the other fraction. Moreover, the parapump system is shown to be capable of continuous operation with a high throughput. In this paper purification of alkaline phosphatase (an enzyme) is experimentally investigated by pH- and ionic-strength-driven parametric pumping. A comparison between the extents of separation obtained wth parametric pumping and the conventional cycling-zone adsorption processes is also presented. Process Description and Experimental Section A human alkaline phosphatase mixture (obtained from Sigma Biochemicals) was chosen to examine experimentally the feasibility of the parametric pumping separation scheme. Alkaline phosphatase has an isoelectric point of 4.5 and a molecular weight approximately equal to 70 OOO. The detailed composition of the proteins in the mixture is unknown. Some of the proteins are thought to be undesirable. Since the enzyme is extracted from the human placental fluid, one major undesired protein is albumin, which unfortunately has an isoelectric point approximately equal to that of alkaline phosphatase. Therefore, a thermodynamic variable other than pH, such as ionic strength, is needed for the purification process. Figure 1 shows the results of a simple experiment for determining the operating conditions (buffer pH and ionic strength) for the parametric pumping process. For this experiment, a chromatographic column was packed with an anionic exchanger (DEAESepharose). Initially, the exchanger was allowed to reach equilibrium with the feed buffer. For pH 7.4, the buffer was a mixture of tris(hydroxymethyl) amionomethane and HC1; for pH 4, it was a mixture of acetic acid and sodium acetate (Colowick and Kaplan, 1955). At t = 0, a feed containing 0.02 wt % of alkaline phosphatase mixture (alkaline phosphatase plus undesired proteins) was introduced at the top of the column. Product samples were collected from the bottom of the column at equal time intervals. The enzyme activity, a, was determined by measuring the increase in absorbance resulting from the hydrolysis of p-nitrophenyl phosphate (Worthington, 1977). The Bio-Rad protein assay was used
Figure 2. Experimental apparatus.
to determine the total protein concentration, y. As shown in Figure 1, the buffer pH and concentration, IS., have pronounced influences on the binding of proteins to the exchanger. At lower pH (case 3 or 4) alkaline phosphatase and most of the undesired proteins carried positive charges; hence, the exit concentrations, up and yp, rose sharply to steady values. At pH 7.4, all proteins in the mixture, including the enzyme, carried negative charges; the product had essentially zero concentration for I S . = 0.1, as in case 1. However, increasing the ionic strength increased the competitions and reduced the interaction between the ion exchanger and the sample substances. Thus, the results for case 2 showed = 0.66 and [Yp/yFlt=,= 0.33, which means that the majority of alkaline phosphatase proteins were unbound on the exchanger while undesired proteins were bound relatively more strongly. Therefore, the enzyme activity per unit weight of total protein in the product stream was higher than that in the feed, i.e., [(up/y )/(aF/yF)] > 1. Based on Figure 1, we have $eveloped a parametric pumping separation scheme. This scheme has three major steps: (I) addition and binding of all proteins in the mixture at pH 7.4 and I S . = 0.1, (11)selective desorption of the desired enzyme at pH 7.4 and IS = 0.6, and (111) regeneration of the ion exchanger at pH 4 and IS. = 0.1. Figure 2 shows schematically the experimental apparatus used. The column (0.016 m i.d. and 0.08 m height) was packed with DEAE Sepharose (registrated trademark) anion exchanger manufactured by Pharmacia Fine Chemicals), and was maintained at a constant temperature of 288 K. The top reservoir was kept at pH 7.4 by an automatic titrator, while a second titrator was used to keep the bottom reservoir at pH 4.0. The buffer ionic strengths in the top and bottom reservoirs were maintained, respectively, at 0.6 and 0.1, by means of two hollow-fiber dialyzers manufactured by Amicon. The feed, containing 0.0290 alkaline phosphatase mixture at pH 7.4 and I.S.= 0.1, was directed to the top of the column. Two elution buffers,
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981 173 STARTOF STARTOF STARTOF STARTOF TOP FEED
DOWN
C~rcdollon
% W D Bcmnwlu
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I
STARTOF STARTOF STARTOF STARTOF C~rc~lotlon%WlW TOP FEED
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a:
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:
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:
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TOP RESERVOIR PHi7.4 .IS=0.6 TOP PRODUCT (ENZYME ENRICHEOI TOP BUFFER PH = 4.0.1S=0.1 I
'
BOTTOM WWER PH.7.4.IS.0.6
,
,
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BOTTOM PRODUCT IPROTEINS FREE)
I
BPI I 1 ..I
C
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PURIFICATION FACTOR IPF) j O :
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BOTTOM RESERVOIR
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40
74
IS
01
01
74
-
74
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06
-
-
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01
01
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14 I 05
I/
SE-
= COUNTER ION = Enzyme with nepotivcchorpe U - B Ut : Undesired PROTEINS ieipec11veIy with negative ond positive charge ANION EXCHANGER
Figure 4. Experimental results for the parametric pumping system.
Figure 3. Schematic description of parametric pumping principle.
one with pH 7.4 and I.S. = 0.6, and the other with pH 4.0 and I.S. = 0.1, were fed to the bottom and top of the column, respectively. Three product streams were withdrawn from the column: top product (enzyme enriched), bottom product (2) (undesired proteins enriched), and bottom product (1) (protein-free). At t = 0, the void volume of the bed is filled with buffer of pH 4 and IS. = 0.1, and the top reservoir is filled with a buffer of pH 7.4 and IS = 0.6. The flow system has seven distinct stages in each cycle, as in Figure 3. (1)The enzyme mixture at pH 7.4 and I S . = 0.1 enters the top of the column for tl time units, while the solution emerging from the other end of the column enters the bottom reservoir. The volume of the feed, Qtl,is set equal to the void volume of the column V,, that is Qtl = V,. As a result of this replacement, the pH of the fluid in column is changed from 4 to 7.4, and the counterions, S-, are exchanged for both E- (enzyme) and U-(undesired protein) present in the feed. (2) The fluid in the top reservoir at pH 7.4 and I S . = 0.6 enters the top of the column for t 2 time units, and simultaneously, a bottom product (1)free of E and U is removed from the column at the same rate. (3) Circulate the fluid between the top reservoir and the column for t3 time units. This will allow the buffer concentration in the column I.S. to change from 0.1 to 0.6. Increasing the IS reduces the interaction between the exchanger and E, causing their elution. (4) Pump the bottom buffer (pH 7.4 and IS. = 0.6) to the bottom of the column for time tl, while a top product containing only pure E- is removed from the column. (5) Pump the bottom reservoir solution at pH 4 and I.S. = 0.1 to the bottom of the column during time interval tl; at the same time solution emerges from the other end and enters the top reservoir.
(6) Circulate the fluid between the bottom reservoir and the column for t6 time units. This will ensure that the pH and I.S. in the column are shifted back to 4 and 0.1, respectively. Thus, desorption of U+ occurs, and S-shifts back to the bed. The ion exchanger is then regenerated. (7) Pump the top buffer at pH 4.0 and I S . = 0.1 to the top of the column during t7. A bottom product, BP(2), containing only U+ is withdrawn from the bottom. One whole cycle is thus completed. From Figure 3, one can see that all of E and U supplied by the feed moves toward the top and bottom product streams, respectively. Complete split of E and U is achieved during one single complete cycle. This result is based on the following assumptions: the ion exchanger used has high capacity, and the ionic exchange between the counterion and the protein (either E or U)is essentially complete at the end of the stages 1, 3, and 6 (Figure 3). In practice, it may not be possible to implement the operating conditions that perfectly satisfy the above assumptions. However, a good separation is attainable by repeating the process illustrated in Figure 3 in succeeding cycles. Results and Discussion Parametric pump separation experiments for various conditions were carried out in the apparatus depicted in Figure 2. The results for a typical run are shown in Figure 4. These results confirm the theory described above. Enzyme (alkaline phosphatase) migrates upward and accumulates at the top of the bed. Figure 4 shows (a),/aF (activity in the product stream/activity in the feed) and (y),/yF (total protein in the product stream/total protein in the feed) as a function of the number of cycles, n. For the bottom product PB(l), the activity and total protein concentration are essentially zero. However, for the top product, the activity increases
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
174
Table I parametric
at steady state ( n - ) pumping purification factor, P.F. 2.8 % enzyme activity recovered, $ 75% rate of production of product 0.065 (based on column height = 8 cm and column diameter = 1.6 cm), international units/min 4
a
I
Yr
3.5:
I
D
0
Or
r.
YP YF
15
30
45
60
75
90
105
20
135
l,mi"Yles
Figure 5. Experimental results for the cycling-zone adsorption.
with n (Figure 4A), and a low total protein is observed (Figure 4B). The reverse holds true for the bottom product, PB(2). This implies that the enzyme and undesired protein move in opposite directions and concentrate in the top and bottom product (2) streams, respectively. The purification factor, P.F., is plotted vs. n in Figure 4C. The P.F. is defined as the ratio of the activity per unit of total protein in the product to that in the feed &e., P.F. = ( ~ / y ) ~ / ( ~ / yP. ) ~F.) values . as high as 3 are obtained in the top product. Note that the feed activity per milligram of enzyme mixture is approximately 2.5 units. The enzyme activity recovered, I), is also shown in Figure 4A. $ is equal to the quantity of enzyme remaining in the top product (the purified stream) compared to that in the feed, Le., $ = PT (u),/FaF. Since PT = F = Qtl (Figure 3), I)= (u),/uF (=0.75 in Figure 4A). Figure 5 shows the results for a conventional cyclingzone process (Baker and Pigford, 1971; Busbice and Wankat, 1975). The difference between the cycling-zone adsorption system and parametric pumping is only in the method of operation. The cycling-zone adsorption flows in a single direction. The basic apparatus consists of a chromatographic column with an inlet stream arranged so that its buffer pH and I S . and enzyme concentration are varied periodically as shown in Figure 5A and 5B. A product stream is withdrawn from the bottom of the column. The product is time dependent in that the concentrations (up and y,) vary continuously. However, the apparatus will eventually reach a repeating state where the product concentrations, up and yp,.repeat from cycle to cycle. In order to make a comparlson with parametric pumping, we set T~ = T~ = T~ = tl (Figures 3 and 5A). The average values of up and yp over each time interval, t l , are used for such comparison. For each cycle, there are three average values (cy1, a2,cy3 and pl, pz, p3 shown in Figures 5C and 5D, respectively) corresponding to three product concentrations. The results for the purified product stream
cyclingzone
adsorption 1.6a 59%b
0.121
on a 2 . Based on ( ~ ~ 1 0 ~Based .
for the two processes are shown in Table I. One can see that parametric pumping has a higher purification factor and greater percent enzyme activity recovered than cyclic-zone systems, while the latter case has a larger rate of production of product. Small molecules in the enzyme mixture can be easily removed by dialysis. However, the removal of large molecules (undesired proteins) represents a real problem. It is a common practice to express the degree of purification in terms of activity in relation to the total protein in the mixture. Therefore, it is important to maximize the quantity a / y , i.e., P.F. Note that the activity, a, is simply a measure of enzyme concentration and is expressed as international units per cubic centimeter of the mixture. Many enzyme separation processes are batchwise. Parametric pumping described here offers the possibility of semicontinuousprocessing, thereby tending to minimize both processing time and degradation. Furthermore, the process can yield high purification factors using small equipment. Acknowledgment The National Science Foundation (CPE 79-10540) provided financial support for this research. Nomenclature a = activity, international unit/mg or cm3 F = feed, cm3 h = column height, m 1.5. = buffer concentration, g-mol/L n = number of cycles of pump operation P T = top product, cm3 Q = volumetric flow rate, cm3/min t = time duration, min VB = bottom reservoir dead volume, cm3 VT = top reservoir dead volume, cm3 V, = column void volume, cm3 y = total protein concentration, g/cm3 $ = enzyme activity recovered ( ) = average value Subscripts n = nth cycle F = feed p = product = steady state Literature Cited Baker, 8.; Pigtord, R. L. I d . Eng. Chem. Fundsm. 1971, 70, 283. Busbice, M. E.;Wankat, P. C. J. Chromalogf. 1975. 774, 639. Chen, H. T.; Hsieh, T. K.; Lee, H. C.; Hill, F. B. AIChE J. 1977, 23, 695. Chen, H. T.; Wong, Y. W.; Wu, S. AIChE J. 1979, 25, 320. Colowick, S. P.; Kaplan, N. 0. "Methods in Enzymology", VoI. I, Academlc Press: New York, 1955;p 143. Shaffer, A. G.;Hamrin. C. E. AlChE J. 1975. 27. 782. Worthington Biochemical Corporation, Enzyme Manual, 1977.
Department of Chemical Engineering New Jersey Institute of Technology Newark, New Jersey 07102
Hung T. Chen* Zikri M. Ahmed Victor Rollen
Received for review April 21,1980 Accepted December 29, 1980
