staging of affinity ultrafiltration processes for chiral separations

Journal of Membrane Science 209 (2002) 107–119

Staging of affinity ultrafiltration processes for chiral separations

Jonathan Romero, Andrew L. Zydney∗Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA

Received 15 January 2002; received in revised form 23 April 2002; accepted 6 May 2002

Abstract

Affinity ultrafiltration using a large stereospecific binding agent can be used to separate enantiomeric mixtures; however,the overall yield and purification factor have generally been inadequate for commercial separations. The objective of thisstudy was to examine the performance of a multi-stage diafiltration process for chiral separations. Data were obtained for theseparation ofd- andl-tryptophan using bovine serum albumin (BSA) as the affinity macroligand. Tangential flow filtration(TFF) was conducted with laboratory scale modules that are linearly scalable to industrial operation. The two-stage system gavepurification factors of more than 20 at greater than 90% yield. Theoretical calculations based on a two site competitive bindingmodel were in good agreement with the experimental data. Purification-yield diagrams were used to examine the effects ofthe ligand concentration, number of stages, and stage volume on the overall separation. The results clearly demonstrate thatmulti-stage affinity ultrafiltration processes can provide high purification factors and yield for enantiomeric separations.© 2002 Elsevier Science B.V. All rights reserved.

Keywords:Ultrafiltration; Tryptophan; Affinity; Chiral; Staging

1. Introduction

There is growing commercial interest in the pro-duction of single enantiomeric versions of manychiral pharmaceuticals, insecticides, pesticides, andnutraceuticals because of the large differences in bi-ological activity and/or toxicity of the different enan-tiomers[1,2]. For example, the (S,S)-diastereomer ofethambutole is effective in the treatment of tubercu-losis, but the (R,R)-diastereomer can cause blurredvision, eye pain, and in some cases complete blind-ness [3]. Many drugs that were originally sold asracemic mixtures have now been re-released as

∗ Corresponding author. Present address: Department of Chem-ical Engineering, The Pennsylvania State University, UniversityPark, PA 16802, USA. Tel.:+1-814-863-7113;fax: +1-814-865-7846.E-mail address:[email protected] (A.L. Zydney).

purified single enantiomers. In 2000, the worldwidemarket for single-enantiomeric drugs was in excessof US$ 130 billion and 40% of all dosage-form drugsales were of single enantiomers[3].

Although many single enantiomer drugs are pro-duced by stereoselective synthesis, there is also agrowing need for separation techniques appropriatefor the large-scale resolution (purification) of chiralmolecules. The most widely used methods for theseparation of racemic mixtures are chromatography[4,5], crystallization[6,7], partitioning[8], and stere-oselective transformation[9]. Affinity ultrafiltration isa potentially attractive alternative to these technolo-gies. Affinity ultrafiltration uses a large stereospecificbinding agent in free solution to selectively bind, andthus retain by a semi-permeable membrane, one ofthe stereoisomers[10–14]. Several investigators havedemonstrated the feasibility of this process, althoughin most of these studies data were only obtained

0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0376-7388(02)00283-1

108 J. Romero, A.L. Zydney / Journal of Membrane Science 209 (2002) 107–119

Nomenclature

CL,j total concentration of affinity ligand in stage “j” (M)Cf ,i,j filtrate concentration ofd- or l-tryptophan leaving stage “j” (M)C̄f ,i,N average concentration in the final filtrate from anN-stage diafiltration (M)CT,i,j total concentration (free+ bound) ofd- or l-tryptophan in stage “j” (M)CT,i,feed initial total concentration ofd- or l-tryptophan in feed solution (M)fi,j fraction of boundd- or l-tryptophan (Cj

b,i/CjT,i) in stage “j”

Ki intrinsic stereoselective binding constant ford- or l-tryptophan (M−1)K2 intrinsic non-stereospecific (secondary) binding constant (M−1)n1 number of stereospecific binding sites on BSAn2 number of non-stereospecific (secondary) binding sites on BSAN number of stages in a multi-staged cascaded affinity diafiltration processND number of diavolumes based on total retentate volumePi purification factor ofd- or l-tryptophanQ volumetric filtrate flowrate (m3/s)Si,j sieving coefficient ford- or l-tryptophan for stagejt filtration time (s)Vj volume of retentate for stage “j” (m3)Vf total volume of collected filtrate (m3)Yi yield of d- or l-tryptophan

Greek letters�j intrinsic selectivity or separation factor for stagejβi,j process coefficient ford- or l-tryptophan in stagej (s−1)

for the instantaneous selectivity during a differentialfiltration process.

Romero and Zydney[13] studied the separa-tion of d- and l-tryptophan by affinity ultrafil-tration using bovine serum albumin (BSA) as astereoselective-binding agent. They were able toobtain 50-fold purification ofl-tryptophan, but theproduct yield was less than 50%. Higher yields couldbe achieved ford-tryptophan in the permeate solu-tion, but the purification factor for this enantiomerwas less than five-fold. Poncet et al.[12] also ex-amined the use of affinity ultrafiltration for the sep-aration of tryptophan enantiomers, with the optimalprocess giving 91% purity and 89% recovery of thed-tryptophan. However, no details were provided onthe process configuration actually used to achieve thisseparation.

Although these results are encouraging, the yieldand purification in these affinity ultrafiltration sys-tems remain well below the levels obtained with highperformance affinity chromatography due to the large

number of equivalent plates (or stages) in the chro-matographic columns. One approach that can be usedto enhance the performance of the affinity ultrafil-tration process is to use a multi-stage cascade. Donget al. [15] have theoretically examined the behaviorof multi-stage affinity ultrafiltration processes forprotein purification under conditions where the im-purities had absolutely no binding interactions withthe large affinity ligand. Model calculations clearlydemonstrated the potential benefits of the staging,although no experimental results were provided tosupport the theoretical analysis.

The objective of this study was to examine the ef-fects of staging on the yield and purification factor forthe separation of racemic mixtures using an affinitydiafiltration process. Experimental data were obtainedfor the separation ofd- andl-tryptophan using BSAas the large stereoselective ligand. Model calculationsexplicitly accounted for competitive binding interac-tions between thed- and l-tryptophan and the BSAligand. Purification-yield diagrams were constructed

J. Romero, A.L. Zydney / Journal of Membrane Science 209 (2002) 107–119 109

for the multi-stage affinity ultrafiltration process, withthe results used to examine the effects of ligand con-centration, number of stages, and stage volume on theoverall separation performance.

2. Theoretical development

Fig. 1 shows a schematic of a two-stage affinitydiafiltration process for the separation of chiral com-pounds. The first reservoir contains the initial feedsolution with both enantiomers along with the largeaffinity macroligand. This solution is circulatedthrough a tangential flow filtration (TFF) modulehaving a membrane that is fully retentive to the largemacroligand and nearly (or completely) permeable tothe small enantiomers. The retentate from the TFFdevice is returned to the feed tank while the filtratepasses to a second membrane stage. Diafiltration

Fig. 1. Schematic of the two-stage affinity diafiltration process.

buffer is added to the first stage at the same rateat which the filtrate is removed, thus maintaining aconstant volume in the feed reservoir throughout theprocess. This approach eliminates problems associ-ated with the build-up of a high concentration of theretained macroligand in the retentate reservoir[13].The reservoirs in the second, and any subsequent,stages are initially filled with solution containing onlythe affinity macroligand. The filtrate flowrate leavingeach of these stages is set equal to the filtrate flowratefrom the first stage, maintaining constant reservoirvolumes throughout the system.

The bulk of the more highly bound enantiomer in theaffinity ultrafiltration process will be retained withinthe first stage. However, any small amount of thisenantiomer that leaks through the first TFF membranewill bind to the affinity macroligand in the secondreservoir and will thus be largely retained within thesecond stage. The net result is a significant increase in


recovery (within the retentate solution) for the morehighly bound enantiomer. The less bound enantiomerwill pass through both membranes, with the recov-ery of this compound in the final filtrate increasingthroughout the affinity diafiltration process. Additionalstages could be added to the system to achieve evenhigher yields and purification, although with consid-erable added complexity.

The mass balance for each stage of the diafiltrationsystem can be written as:

dCT,i,j

dt= − Q

Vj

[Cf ,i,j − Cf ,i,j−1] (1)

where CT,i,j is the total concentration (bound+unbound) of enantiomeri in stagej, Vj is the volumeof the solution in the retentate reservoir in stagej, andQ the constant volumetric filtrate flowrate throughthe system.Cf ,i,j is the filtrate concentration leavingstagej, with Cf ,i,0 = 0 since the diafiltration flowinto the first stage is pure buffer.

In order to integrateEq. (1), it is first necessary toexpress the filtrate concentration leaving each stage interms of the total feed concentration in that stage:

Cf ,i,j

CT,i,j

= Si,j (1 − fi,j ) (2)

where fi,j is the fraction of the enantiomer that isbound by the affinity ligand andSi,j is the observedsieving coefficient for the free enantiomer. For thesmall tryptophan molecules examined in this study,Si,j = 1, i.e. the concentration of the free tryptophanin the filtrate and the feed solutions are essentiallyequal.

The intrinsic selectivity or separation factor for eachstage in the affinity ultrafiltration process is defined as:

αj = Cf ,D,j /CT,D,j

Cf ,L,j /CT,L,j

= SD,j (1 − fD,j )

SL,j (1 − fL,j )(3)

High intrinsic selectivities thus require very strongbinding of the retentate product (fi,j ≈ 1) with onlyminimal (or moderate) binding of the filtrate product,in this case thed-tryptophan.

Unlike the behavior in many multi-stage systems,the intrinsic selectivity or separation factor for themulti-stage affinity diafiltration process is not sim-ply equal to the product of the selectivities for theindividual stages. For example, if the enantiomersare primarily located in theNth (last) stage, then the

concentrations in the final (filtrate) product will bedetermined completely by the binding characteristicsof this final stage, irrespective of the binding behavioror concentrations in any of the preceding stages. Notethat near the start of the diafiltration, where both enan-tiomers are present at significant levels only in thefirst (feed) stage, the overall selectivity of the processdoes become equal to the product of theαj valuessince the feed concentration in each subsequent stageis directly proportional to the filtrate concentrationleaving the preceding stage.

In general,Eqs. (1) and (2)must be integratednumerically since the fraction of bound enantiomer(fi,j ) changes with time due to the dependence ofthe binding equilibrium on the concentrations of bothenantiomers. Under conditions where thefi,j re-main approximately constant during the diafiltration,Eqs. (1) and (2)can be integrated analytically to give:

CT,i,1

CT,i,feed= exp[−βi,1t ] (4)

CT,i,2

CT,i,feed= V1

V2

(βi,1

βi,2 − βi,1

)

× [exp(−βi,1t) − exp(−βi,2t)] (5)

where

βi,j = QSi,j (1 − fi,j )

Vj

(6)

Similar equations can be developed for the concentra-tions in the subsequent stages in a multi-stage system,with the results expressed as the sum of a series of de-caying exponentials involving theβi,j for the differentstages.

The yield of the less bound enantiomer in the filtratecollected from the final stage is:

YD =∫ t

0QCT,D,N (1 − fD,N )dt

V1CT,D,feed

= 1 +(

βD,1

βD,2 − βD,1

)exp(−βD,2t)

−(

βD,2

βD,2 − βD,1

)exp(−βD,1t) (7)

where the second expression on the right-hand side isvalid for a two-stage system under conditions wherethe fi,j are constant. The purification factor for thed-tryptophan is given as:


PD =(∫ t

0QCTD,N (1 − fD,N )dt)

/(V1CTD,feed

)(∫ t

0QCTL,N (1 − fL,N )dt)

/(V1CTL,feed

)

=1 + [βD,1/(βD,2 − βD,1)]exp(−βD,2t)

−[βD,2/(βD,2 − βD,1)]exp(−βD,1t)

1 + [βL,1/(βL,2 − βL,1)]exp(−βL,2t)

−[βL,2/(βL,2 − βL,1)]exp(−βL,1t)

(8)

where again the second expression is valid for atwo-stage system with constantfi,j . Thus, the yieldfor thed-tryptophan in the collected filtrate begins atzero and increases throughout the diafiltration pro-cess, while the purification factor decreases as moreof thel-tryptophan passes into the filtrate. The initial(maximum) purification factor, evaluated by takingthe limit of Eq. (8)ast → 0, is:

P maxD = βD,1βD,2

βL,1βL,2(9)

which is simply equal to the product of the intrinsicselectivities for the two stages. The corresponding ex-pression for a process containingN stages is given bythe product of theαj for all N stages.

N∏j=1

αj =N∏

j=1

βD,j

βL,j

(10)

The yield for the more highly bound enantiomercollected at the end of the process by pooling the re-tentate solutions from the multiple stages is:

YL =∑N

j=1VjCT,L,j

V1CT,L,feed

= (βL,2/(βL,2 − βL,1))exp(−βL,1t)

− (βL,1/(βL,2 − βL,1))exp(−βL,2t) (11)

with the purification factor given as:

PL =∑N

j=1VjCT,L,j∑Nj=1VjCT,D,j

(CT,D,feed

CT,L,feed

)

=[βL,2/(βL,2 − βL,1)]exp(−βL,1t)

−[βL,1/(βL,2 − βL,1)]exp(−βL,2t)

[βD,2/(βD,2 − βD,1)]exp(−βD,1t)

−[βD,1/(βD,2 − βD,1)]exp(−βD,2t)

(12)

The yield of l-tryptophan decreases throughout thediafiltration as small amounts of this enantiomer leak

through the membranes and into the final filtrate. How-ever, the purification factor continually increases dueto the much more rapid removal of the less-stronglyboundd-enantiomer.

Rigorous calculations for the purification factorand yield were performed by numerically integrat-ing Eqs. (1) and (2)using a forward finite differencescheme implemented on MATLAB version 6.1. Thebinding fractions were calculated at each time-stepbased on the total concentration ofd- andl-tryptophanin each stage using the two-site competitive bindingmodel presented inAppendix A.

3. Materials and methods

Racemic mixtures ofd- and l-tryptophan, alongwith the purified enantiomers, were obtained fromSigma Chemical (catalog #T-3300, T-8629, T-9753,St. Louis, MO). The tryptophan was dissolved in10 mM borate buffer (pH 9.1) prepared from sodiumtetraborate (Fisher Scientific) in deionized distilledwater (resistivity >18 Mohm cm) obtained from aBarnstead water purification system (Dubuque, IA).All buffer solutions were prefiltered through 0.2�mSupor®-200 microfiltration membranes (GelmanSciences, Ann Arbor, MI) to remove particulatesprior to use. BSA (Sigma A-8022) was used as thestereoselective-binding agent. BSA was added to thetryptophan solution to give a final protein concen-tration ranging from 0.30 mM (21 g/l) to 0.60 mM(41 g/l). The resulting solutions were gently stirredfor approximately 2.5 h to ensure adequate mixingand equilibrium binding of the tryptophan. The pHof the final solution was 8.5 as measured using anAcumet 915 pH meter (Fisher Scientific).

Tryptophan concentrations were evaluated by cap-illary zone electrophoresis using�-cyclodextrine(Sigma C-4642) as a chiral resolving agent. A 50 mMsolution of �-cyclodextrine in 50 mM phosphatebuffer at pH 2.2 was used as the background elec-trolyte. Electrophoresis was performed using an ISCOmodel 3850 capillary electropherograph (ISCO Inc.,Lincoln, NB) equipped with a dual-polarity vari-able high-voltage dc power supply and a variablewavelength UV–VIS absorbance detector. Data wereobtained using a 50 cm long fused silica capillary(CElect-FS75 CE column; 362�m o.d., 75�m i.d.)


with an applied voltage ranging from 13 to 17 kV.Tryptophan detection was at 278 nm, with the con-centration determined from the area under the elec-tropherograms.

Tryptophan concentrations in the presence ofBSA were evaluated by first adding 13�l of a 1 MHCl/0.2 M KCl solution to a 1 ml sample. This lowpH eliminates essentially all tryptophan binding to thepositively charged BSA[16]. The resulting solutionwas then filtered through a 30,000 molecular weightcutoff membrane to remove the BSA. Thed- andl-tryptophan concentrations in the collected filtratewere measured by capillary zone electrophoresis asdiscussed previously.

All filtration experiments were performed withBiomax polyethersulfone membranes (MilliporeCorp., Bedford, MA) having a nominal molecularweight cutoff of 30,000 g/mol that were fully re-tentive to the BSA. Flat sheet membranes were cutinto 25 mm diameter disks for use in the stirred cell.Diafiltration experiments were performed using Pel-licon XL TFF modules having 50 cm2 of membrane(lot PXB030A50). All membranes were thoroughlyflushed with deionized distilled water prior to use toremove any glycerin, which is used as a wetting andstorage agent.

3.1. Competitive binding experiments

The binding constants forl- andd-tryptophan wereevaluated using a 25 mm diameter stirred UF cell(model 8010, Amicon Corporation, Beverly, MA).The device was filled with a mixture of BSA andtryptophan of known concentrations. The stirrer wasset to 550 rpm using a Strobotac type 1531-AB strobelight (General Radio Co., Concord, MA). The devicewas air pressurized, and filtrate and bulk samples wereobtained periodically for off-line evaluation of thetryptophan concentrations. Data were analyzed usingthe competitive two-site binding model described inAppendix A:

(1−fi)−1 = n1KiCL

1+KLCT,L(1−fL)+KDCT,D(1−fD)

+ n2K2CL

1+K2CT,L(1−fL)+K2CT,D(1−fD)

+ 1 (13)

whereCL is the total BSA concentration,n1 andn2 arethe number of primary and secondary binding sites oneach BSA molecule,KL andKD are the equilibriumbinding constants for the stereospecific site, andK2 isthe binding constant for the non-stereospecific site.

3.2. Affinity diafiltration experiments

Both single-stage and two-stage diafiltration runswere performed using the Pellicon XL TFF mod-ules. Both retentate reservoirs were filled with a BSAsolution with the tryptophan mixture added to thefeed (first) reservoir. The filtrate lines were initiallyreturned directly to the corresponding feed tank, al-lowing the system to run in total recycle mode withno connection between the two stages until the sys-tem had stabilized. The feed flowrate in each stagewas controlled separately with a peristaltic pump(Rabbit-Plus, Rainin, MA).

After the system had stabilized, the pumps werestopped and the filtrate line from stage 1 was re-directed so that it became the feed to stage 2 (Fig. 1).The filtrate line from stage 2 was then placed into thefinal collection reservoir. The diafiltration reservoirwas filled with a 0.01 M sodium tetraborate solution,with the exit from the reservoir connected to the inletof stage 1. Both retentate reservoirs were sealed, andthe feed pumps were re-started. This generated a vac-uum in the two solution reservoirs, with the retentatevolumes maintained constant by the siphoning of fluidfrom the diafiltration reservoir into stage 1 and thenfrom stage 1 into stage 2. In principle, both membraneunits should provide equivalent filtrate flowrates atthe same feed flowrate setting (equal pump speeds),but small differences in module construction andmembrane properties led to slight variations betweenstages. In general, the feed flowrate to stage 1 wasset at a higher value than the feed flowrate to stage 2.However, any fluctuations in the filtrate flowrate leav-ing stage 2 were compensated for by an equivalentchange in flowrate from stage 1 due to the pressureadjustments through the interconnected reservoirs.The net result was that the volumes in each reservoirremained essentially constant throughout the diafiltra-tion irrespective of any fluctuations in the flowrates.The filtrate from the final stage was collected con-tinuously, with small samples taken for subsequentanalysis of thel- and d-tryptophan concentrations.


Samples were also taken periodically from the recyclestream from each reservoir to verify the overall massbalance in the system.

4. Results and analysis

Experimental results for the intrinsic binding se-lectivity of BSA for l- and d-tryptophan are shownin Fig. 2. Data were obtained in the stirred cell us-ing racemic solutions of the tryptophan enantiomersat constant BSA concentrations of 0.3 and 0.6 mM.The selectivity was calculated usingEq. (3), withthe concentration of the free tryptophan evaluatedfrom the filtrate samples while the ratio of totald- tol-tryptophan concentration in the stirred cell was equalto one for the racemic mixtures. The solid curves aremodel calculations, which account for the competitivebinding of d- andl-tryptophan to both a stereoselec-tive binding site and a non-stereoselective site on BSAas discussed inAppendix A. The selectivity increases

Fig. 2. Intrinsic selectivity as function of the total tryptophan concentration at BSA concentrations of 0.3 mM (solid circles) and 0.6 mM(solid squares). Model binding parameters areKL = 39,240 M−1, KD = 516 M−1, n1 = 0.82, n2 = 2, andK2 = 300 M−1.

with decreasing tryptophan concentration due to thegreater availability of the stereoselective binding site.For example, the selectivity increases fromα < 2 athigh tryptophan concentrations to aboutα = 7 forthe 0.3 mM BSA solution andα = 10 for the 0.6 mMBSA for tryptophan concentrations below 0.3 mM.

The data inFig. 2 clearly demonstrate that BSAcan provide a stereoselective separation of trypto-phan enantiomers. Diafiltration processes were thusperformed using both a one-stage (top graph) andtwo-stage (bottom graph) system. The one-stage sys-tem had 80 ml of feed solution containing 48�molof BSA (0.6 mM concentration) and 12�mol of bothd- and l-tryptophan (0.15 mM concentration). Thetwo-stage system had a 20 ml feed containing thesame mass of tryptophan (0.6 mM concentration inthe feed reservoir) and the same total mass of BSA(split so that the BSA concentration was 1.2 mM inthe first stage and 0.8 mM in the 30 ml second stage).The filtrate flowrate in both systems was maintainedat approximately 4.2 × 10−9 m3/s (corresponding to


Fig. 3. Filtrate concentration vs. process time ford- andl-tryptophan in a single-stage (top panel) and two-stage (bottompanel) system. Solid and dashed curves are model predictionsdescribed in the text.

a filtrate flux of 8.3 × 10−7 m/s) using appropriateroller pumps.

The filtrate concentrations in the one-stage system(top panel ofFig. 3) decrease monotonically through-out the diafiltration due to the continuous removalof d- and l-tryptophan from the feed reservoir. Theinitial filtrate concentration ofd-tryptophan is muchlarger than that for thel-enantiomer due to the muchstronger binding of thel-tryptophan by BSA. The

ratio of the filtrate concentrations at the start of theprocess is simply equal to the intrinsic selectivity sincethe initial total concentrations ofd- andl-tryptophanin the solution reservoir are equal. At long times, theconcentration ofl-tryptophan in the filtrate solutionbegins to exceed that for thed-tryptophan since mostof the d-tryptophan has been removed from the feedreservoir.

In contrast to the results for the one-stage system,the filtrate concentrations ofd- andl-tryptophan leav-ing the second stage of the two-stage system (bottompanel of Fig. 3) start at zero and initially increasewith time as the enantiomers are filtered out of thefirst stage and begin to accumulate in the second. Thed-tryptophan accumulates much more rapidly thanthe l-tryptophan, leading to a much more rapid risein the concentration of thed-enantiomer in the fil-trate stream. Thed-tryptophan is eventually washedthrough the system, leading to a reduction in theconcentration of this enantiomer in the second stageretentate solution and a corresponding maximum inthe exiting filtrate concentration as seen in the lowerpanel ofFig. 3. This maximum is not observed forthel-tryptophan during the course of the diafiltrationsince the high retention ofl-tryptophan in the firststage leads to a much slower accumulation of thisenantiomer in the second stage.

The solid curves inFig. 3 represent model calcu-lations developed by numerical solution ofEqs. (1)and (2)while the dashed curves represent the analyt-ical results evaluated assuming that thefi,j remainconstant at their initial values. In both the cases, themodel calculations were true predictions based on thevalues of the binding parameters determined previ-ously from the results inFig. 2 (Appendix A). Theinitial values offi,j for the second stage were eval-uated from the binding model by taking the limit asthe concentrations of bothd- andl-tryptophan go tozero. Thus, the initial extent ofl-tryptophan bindingin the second stage (fL,2 = 0.96) is larger than that inthe first stage (fL,1 = 0.94). The full numerical solu-tion is in good agreement with the experimental data,properly capturing the decrease ind- andl-tryptophanconcentrations in the one-stage system as well as themaximum in thed-tryptophan concentration in thetwo-stage system. The analytical solution also doesan excellent job describing the filtrate concentrationdata. The good agreement for the single-stage process


occurs because the increase infL andfD that occurredduring the diafiltration was relatively small at the lowfeed tryptophan concentrations used in this experi-ment. For example,fL was predicted to increase onlyfrom 0.93 to 0.94 over the single-stage diafiltration.The binding behavior in the two-stage system is morecomplicated. In this case, bothfL,1 andfD,1 increaseduring the diafiltration due to the reduction in theretentate concentrations in the first stage while thebinding fractions in stage 2 decrease over most ofthe filtration as thed- and l-tryptophan accumulatein the second stage retentate reservoir. These two ef-fects tend to balance out, resulting in the very goodagreement between the full numerical solution andthe analytical approximation developed assuming thatthefi,j remain constant during the diafiltration.

The top panel inFig. 4 shows the correspondingd- and l-tryptophan concentrations in the retentatereservoir of the one-stage system. The retentate con-centrations were calculated from the filtrate data usingthe overall mass balance for the system. Data ob-tained for the retentate concentrations at several timepoints during the diafiltration demonstrated mass bal-ance closure to within 10% for all runs. The solid anddashed curves again represent calculations using thefull numerical model and the analytical solution. Theretentate concentration ford-tryptophan decreasesmuch more rapidly than that forl-tryptophan sincethe l-isomer is more strongly bound to the largemacroligand. The bottom panel shows results for theaverage normalized tryptophan concentration in theretentate solutions from the combined stages 1 and 2of the two-stage system. The average concentrationsdecrease with time as both enantiomers are filtered outof the system, with the rate ofd-tryptophan removalbeing much greater than that ofl-tryptophan. Therate ofl-tryptophan removal in the two-stage systemis much smaller than that seen in the single-stagedevice since the small amount of this enantiomer thatleaks through the first TFF membrane will bind to theaffinity macroligand in the second reservoir and thusbe largely retained within the second stage.

In order to more effectively compare the results inthe one- and two-stage systems, the data inFigs. 3and 4were used to evaluate both the purity and re-covery of d-tryptophan in the filtrate solution as afunction of filtration time, with the results shown inthe top and bottom panels ofFig. 5. The solid and

Fig. 4. Normalized retentate concentration versus process time ford- and l-tryptophan in a single-stage (top panel) and two-stage(bottom panel) system. Solid and dashed curves are model pre-dictions described in the text.

dashed curves are again the model predictions usingthe full numerical solution and the analytical approx-imation with constantfi,j , respectively. The purifica-tion factor decreases throughout the diafiltration dueto the leakage of unboundl-tryptophan through themembrane. In contrast, the yield increases with timeas more of thed-tryptophan is collected in the fil-trate. The initial purification factor for the two-stagesystem (P D = 136) was 14 times larger than that


Fig. 5. Purification factor (top panel) and yield (bottom panel)vs. process time ford-tryptophan. Filled symbols are for asingle-stage system (CT,D,0 = CT,L,0 = 0.15 mM, CL = 0.6 mM,V = 80 ml). Opens symbols are for a two-stage cascade process(CT,D,0 = CT,L,0 = 0.6 mM, CL,1 = 1.2 mM, CL,2 = 0.8 mM,V1 = 20 ml, andV2 = 30 ml). Solid and dashed curves are thenumerical and analytical solutions, respectively.

in the single-stage device (P D = 9.7) due to theextra retention ofl-tryptophan by the BSA bindingin the second stage. However, the overall yield ford-tryptophan in the two-stage system at short timesis less than that in the single-stage process due to

the accumulation ofd-tryptophan in the second stageretentate reservoir. The situation is reversed at longtimes (t > 5 h), with a greater yield ofd-tryptophanin the two-stage system. This seemingly counterintu-itive result arises because the retentate volume in theone-stage system (V = 80 ml) was significantly largerthan the total retentate volume in the two-stage system(V1 + V2 = 50 ml). Since the two systems were op-erated with the same volumetric filtrate flowrate, thetotal number of diavolumes (ratio of collected filtratevolume to total retentate volume) in the two-stagesystem was a factor of 1.6 greater than that in theone-stage process (at the same filtration time).

The inherent trade-offs between the yield and pu-rification factor during the affinity diafiltration areshown more explicitly inFigs. 6 and 7for thed- andl-tryptophan, respectively. Ford-tryptophan (Fig. 6),the diafiltration process begins in the lower right cor-ner with the maximum purification factor and pro-ceeds up and to the left with the purification factordecreasing as the yield ofd-tryptophan in the filtrateincreases. The purification factor–yield curve for the

Fig. 6. Yield versus purification factor ford-tryptophan in thefiltrate solution. Filled symbols are for a single-stage system(CT,D,0 = CT,L,0 = 0.15 mM, CL = 0.6 mM, and V = 80 ml)and open symbols are for a two-stage cascade process (CT,D,0 =CT,L,0 = 0.6 mM, CL,1 = 1.2 mM, CL,2 = 0.8 mM, V1 = 20 ml,and V2 = 30 ml). Solid and dashed curves are the numerical andanalytical solutions, respectively.


Fig. 7. Yield versus purification factor forl-tryptophan in theretentate solution. Filled symbols are for a single-stage system(CT,D,0 = CT,L,0 = 0.15 mM, CL = 0.6 mM, and V = 80 ml)and the open symbols are for a two-stage cascade process(CT,D,0 = CT,L,0 = 0.6 mM, CL,1 = 1.2 mM, CL,2 = 0.8 mM,V1 = 20 ml, andV2 = 30 ml). Solid and dashed curves are thenumerical and analytical solutions, respectively.

two-stage process is shifted significantly to the rightcompared to that for the single-stage system. Thus, fora d-tryptophan yield ofY D = 90% the single-stageprocess provides a purification factor of onlyP D =4.4 (purity = 82%) compared to more than a 20-foldpurification in the two-stage system (corresponding toa final purity ofd-tryptophan of 95%).

The corresponding results forl-tryptophan in theretentate stream are shown inFig. 7. In this case, the di-afiltration process begins in the upper left corner witha product yield of 100%, with the yield decreasingand the purification factor increasing over the courseof the diafiltration due to the much greater removalof the weakly bound impurity (d-tryptophan) from theretentate solution. The product yield at a given purifi-cation factor is much higher in the two-stage systemdue to the extra retention ofl-tryptophan in the sec-ond stage. For example, atP L = 10, the single-stageprocess has only 77% yield compared to less than a5% yield loss for the two-stage process. This allowsthe two-stage process to be run out to much greater

purification while still providing acceptable productyield.

Although the separations inFigs. 3–7used the sameamount of tryptophan, the initial (feed) concentrationof tryptophan in the two-stage system was consider-ably higher than that in the one-stage system to com-pensate for the smaller feed volume.Fig. 8 shows themodel simulations for a given feed solution (V1 =50 ml andCT,i,0 = 0.1 mM) using a fixed and equalconcentration of BSA in stages 1 and 2 for different

Fig. 8. Model simulations of the purification factors forl-tryptophan in the retentate (bottom panel) andd-tryptophan inthe filtrate (top panel) at fixed product yield. Calculations weredone with V1 = 50 ml, CT,i,0 = 0.05 mM, KL = 39,240 M−1,KD = 516 M−1, n1 = 0.82, n2 = 2 andK2 = 300 M−1.


values of the retentate volume for the second reser-voir (V2). Results are shown for three different BSAconcentrations:CL = 0.6, 0.9 and 1.2 mM. The cal-culated purification factors are plotted as function ofV2/V1 determined at a constant yield ofY D = 90% ford-tryptophan in the filtrate (top panel) andY L = 80%for l-tryptophan in the retentate (bottom panel). Thed- and l-tryptophan purification factors increase asthe BSA concentration increases (at constantV2/V1)as a result of the increase in binding capacity forthe l-tryptophan. At very lowV2/V1, the purificationfactor approaches the value for a single-stage systemas expected. AsV2 increases, a much larger volumeof filtrate must be processed to achieve the sameYD(or YL) resulting in a larger washout of the weaklyboundd-tryptophan. This leads to a higher purity ofl-tryptophan in the retentate solution and a higher pu-rity of d-tryptophan in the filtrate. For example, thepurification factor forl-tryptophan at a BSA concen-tration of 1.2 mM increases by 2 orders of magnitudeasV2/V1 increases from 0.02 to 1. However, at largerV2, the purification factor begins to decrease withincreasing volume of the second stage. Under theseconditions, the bulk of the tryptophan in stage 1 iswashed into stage 2 before there is any significantaccumulation of tryptophan in the final filtrate. ForV2 V1, the system again begins to behave like asingle-stage process but now the separation is deter-mined entirely by the properties of the second stage.The optimal purification factor occurs whenV2 issomewhat larger thanV1 sinceα2 is greater thanα1,i.e. under conditions which give more weight to thesecond stage. The location of the maximum thus shiftsto higherV2 as the BSA concentration decreases sincethis causes a larger reduction inα1 thanα2. Similareffects are seen at different tryptophan concentrationswith the purification factor decreasing and the optimalV2/V1 increasing asCT,i,0 increases.

5. Conclusions

Although previous studies have demonstrated thefeasibility of performing affinity chiral separationsusing membrane systems, the yield and purificationin these membrane processes remain below the levelsobtained with high performance affinity chromatog-raphy due to the large number of equivalent plates

(or stages) in the chromatographic columns. The dataand analysis presented in this manuscript providethe first detailed description of a two-stage affinityultrafiltration process for chiral separations using alarge stereoselective macroligand. The data were ob-tained with TFF modules that are linearly scalable tolarge (100 m2) commercial membrane systems[18].The two-stage system provides much better yield andpurification factors due to the extra retention of themore highly boundl-tryptophan in the second stage.The experimental data are in good agreement withmodel predictions developed using independently de-termined binding parameters for the tryptophan–BSAsystem. A simple analytical solution was also devel-oped, based on the assumption of constant bindingfractions throughout the diafiltration, with this so-lution providing an accurate approach to the rapiddesign and optimization of affinity ultrafiltrationsystems.

Preliminary model simulations for a two-stage cas-cade system provide important insights into the designand operation of the affinity ultrafiltration system. Forexample, at a constant product yield, the maximumpurification factor is obtained at a particular ratio ofV2/V1 that varies based on the ligand and feed con-centrations. The overall optimization of the two-stagecascade system is quite complex, involving trade-offsbetween yield and purification and the appropriatechoice of the concentration of the affinity ligand,the ratio of the stage volumes, the detailed bindingequilibria, and the feed characteristics. These latterphenomena will be considered in some detail in futurepublications.

Appendix A. Binding phenomena

Previous studies have shown thatl-tryptophanbinds predominantly to one site on BSA in a highlystereospecific manner and to several secondary siteswith much lower affinity[16,17]. Since the secondarysites(s) are non-stereospecific, it is likely that bothenantiomers would bind competitively with the samebinding constant. Competitive binding studies withracemic tryptophan methyl ester (an analog of tryp-tophan) suggest that the weakly boundd-isomer candisplace thel-isomer at the stereospecific site[16,17].Our binding model thus assumes that bothl- and


d-tryptophan competitively bind to two sites on BSA(P1 and P2):

L + P1KL↔ LP1

D + P1KD↔ DP1

L + P2K2↔ LP2

D + P2K2↔ DP2

(A.1)

where LP and DP are the bound complexes,KL andKD are the equilibrium binding constants for the stere-ospecific site, andK2 is the binding constant for thenon-stereospecific site[16].

In the current analysis, the binding reactions are as-sumed to be very fast compared to the mean residencetime in the membrane device so that equilibrium isachieved throughout the diafiltration. The extent ofbinding is evaluated directly from the binding reac-tions inEq. (A.1)as:

(1−fi)−1 = n1KiCL

1+KLCT,L(1−fL)+KDCT,D(1−fD)

+ n2K2CL

1+K2CT,L(1−fL)+K2CT,D(1−fD)

+ 1 (A.2)

whereCL is the total BSA concentration andn1 andn2 are the number of primary and secondary bindingsites on each BSA molecule.Eq. (A.2) was used inall the model calculations withKL = 39,240 M−1,KD = 516 M−1, n1 = 0.82, K2 = 300 M−1, andn2 = 2 as determined from binding data obtained inthe stirred cell[13].

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staging of affinity ultrafiltration processes for chiral separations

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