BP-2002

Critical Analysis of Lysozyme Refolding Kinetics
A.Mark Buswell and Anton P.J.Middelberg*
Department of Chemical Engineering,University of Cambridge,Pembroke Street,Cambridge CB23RA,U.K.
The kinetics of lysozyme refolding and aggregation is studied using an existing competing first-and third-order reaction scheme.The existing model overestimates yield at high refolding concentrations (>1mg/mL),thus limiting its use for reactor design at industrially relevant refolding concentrations.This study demonstrates that a pathway exists for the incorporation of refolded native protein into aggregates.Specifically,native lysozyme labeled with fluorescein isothiocyanate was added to the refolding buffer prior to dilution refolding of denatured and reduced lysozyme.Aggregates collected from these experiments showed significant fluorescence,indicating that labeled lysozyme had been incorporated into the aggregates during refolding.Although the precise pathway of incorporation has not been elucidated,it is clear from this work that the existing model for lysozyme refolding is not globally applicable.In particular,previous work has analytically demonstrated that neglect of a pathway from native to aggregate can result in the design of a grossly suboptimal reactor strategy.This study demonstrates that such a pathway can exist experimentally and emphasizes the need to critically assess refolding kinetic models before their use in reactor design equations.
Introduction
Protein refolding is an important unit operation during the manufacture of recombinant proteins via the inclu-sion body process route.Inclusion bodies are recovered from the disrupted host cells,and a denaturant and a reducing agent are used for solubilization.The denatured protein is then refolded to its native state by alteration of the solvent environment,often by simply diluting the solubilized inclusion body protein into a suitable buffer.Ideally,the final concentration of protein after dilution should be as high as possible in order to minimize batch volume for subsequent downstream purification.How-ever,aggregation dominates at high protein concentra-tions,and dilution refolding operations therefore usually operate at low concentrations of 10-100µg/mL (1,2).An evaluation of overall process economics shows that protein concentration during refolding can have a major impact on overall manufacturing cost for the inclusion body process route and,in certain instances,can result in a process being economically nonfeasible (3,4).In particular,a reaction pathway allowing incorporation of native protein into aggregates can significantly affect the optimum process operation point,and selection of the wrong operating point through neglect of this pathway can significantly increase annualized cost (3).A difficulty in applying economic analysis to protein refolding opera-tions using the usual reactor design equations is that an accurate kinetic scheme is rarely available for the protein of interest.
The refolding and aggregation reactions are often modeled by a set of competing first-and higher-order kinetic equations (5),assuming the basic reaction scheme shown in Figure 1.Refolding is a monomeric reaction,
while aggregation is multimeric.An analysis of dilution refolding rate data at different overall protein concentra-tions gives a set of apparent refolding and aggregation rate constants (6).These rate constants apply for an effective two-state transition between collapsed protein and correctly refolded and aggregated protein,and thus represent a simplification of the true complexity.Kinetic models of protein refolding have generally only consid-ered irreversible aggregation and refolding with no allowance for a back-reaction of native protein to ag-gregates.A significant back-reaction can have a major impact on the design and operation of economically efficient refolding operations (3).However,experimental demonstration of a significant back-reaction of native protein to aggregates during refolding at high protein concentrations has not,to our knowledge,been reported in the literature.
The first aim of the present study was to investigate the use of an existing kinetic model for lysozyme refolding over a range of concentrations extending to highly aggregating conditions (>1mg/mL),but at a fixed denaturant concentration of 0.5M GdmCl.The kinetics of lysozyme refolding has been extensively studied at reasonably low concentrations (<1mg/mL),where the refolding yield is comparatively high (>40%)(2,6).However,in certain instances industrial refolding opera-tions may operate under conditions where aggregation
*To whom correspondence should be addressed.Telephone:+441223335245.Fax:+441223334796.E-mail:antonm@
.
Figure 1.Simplified kinetic scheme showing first-order refold-ing competing with higher-order aggregation,where k 2is the refolding rate constant and k 3is the aggregation rate constant (6).The dashed arrows represent potential pathways for native protein incorporation into aggregates during refolding.
470Biotechnol.Prog.2002,18,470−475
10.1021/bp0200189CCC:$22.00
©2002American Chemical Society and American Institute of Chemical Engineers
Published on Web 04/25/2002
is the dominant product and refolding yields are below 20%.It was therefore of interest to investigate the accuracy of the existing kinetic model at industrially relevant refolding concentrations.The second aim of the present study was to investigate whether native lysozyme could be incorporated into aggregates during refolding, thereby demonstrating a pathway for the incorporation of refolded native protein back into aggregates.Two potential pathways for this back-reaction are indicated in Figure1by the dashed arrows.To establish the presence of a back-reaction,native lysozyme was labeled with fluorescein isothiocyanate(FITC)and the labeled lysozyme was added to the refolding buffer prior to commencing a refolding test.This mimics the processes occurring in fed-batch refolding,where denatured protein is added to buffer containing renatured(but unlabeled) product.Following renaturation,aggregates were then observed under a fluorescence microscope to establish whether FITC-labeled lysozyme was incorporated from the refolding buffer into the aggregates.Through these studies we demonstrate that the existing kinetic model for lysozyme refolding is an oversimplification that may lead to suboptimal reactor operating strategy when used in conjunction with standard reactor-design equations. This result has implications for the refolding of proteins other than lysozyme.
Experimental Methods
Materials.Urea,ethylinediaminetetraacetic acid (EDTA),Tris,oxidized glutathione(GSSG),hydrochloric acid(HCl),sodium hydroxide(NaOH),potassium hy-droxide(KOH),iodoacetic acid(IDA),monobasic sodium phosphate,dibasic sodium phosphate,and Micrococcus lysodeikticus(M.lysodeikticus)were from Sigma.Guani-dinium chloride(GdmCl)and dithiothreitol(DTT)were from Melford Laboratories Ltd.Ultrapure water was used for the preparation of all solutions.HPLC grade aceto-nitrile and trifluoroacetic acid(TFA)were from Merck. BioChemika hen egg white lysozyme was from Fluka(No. 62971).
Protein Concentration.The concentration of native and denatured-reduced lysozyme was calculated on the basis of absorbance at280nm using an extinction coefficient of2.63or2.37cm‚mL‚mg-1,respectively(7). Native lysozyme samples were diluted in the same buffer as they were originally prepared in.Denatured lysozyme samples were diluted into0.1M acetic acid(7). Enzymatic Activity.The enzymatic activity of samples from the refolding experiments was measured at ambient temperature by following the decrease in absorbance at 450nm(Unicam UV1Spectrophotometer)of a cell suspension(0.15mg/mL M.lysodeikticus,0.067M sodium phosphate,pH6).Samples were collected during the refolding experiments at various intervals and quenched in order to arrest the refolding reaction by adding30µL of10%TFA to270µL of sample.The samples were further diluted with acidified TE buffer(1%TFA,50mM Tris,1mM EDTA)to a total protein concentration of0.1 mg/mL.A20µL aliquot of the diluted sample was added to980µL of cell suspension,giving a total protein concentration of2µg/mL,and briefly mixed.After5s the absorbance was monitored for30s.A linear decrease in aborbance was observed.The percent of native protein was calculated as the ratio of the slope of the absorbance decay of the sample to the slope of a native lysozyme standard.The effectiveness of the quenching procedure using TFA was confirmed by comparing the enzymatic activity of samples quenched with TFA,and stored at4°C overnight,to that of samples analyzed immediately without quenching and to that of samples quenched using 0.5M IDA in0.5M KOH and0.5M Tris(6).The three methods gave the same enzymatic activity(data not shown).In general,quenched samples were stored at4°C until analysis,which was performed on the same day. HPLC Analysis.Quenched samples from the refolding experiments were also analyzed using a C5reversed-phase column(5µm,300Å,150mm×4.6mm,Jupiter, Phenomenex)on a high-performance liquid chromatog-raphy(HPLC)system comprising a X-Act4-Channel degassing unit(Jour Research),a7725I injection valve (Rheodyne),two HPLC422pumps(Kontron Instru-ments),a C030HPLC column chiller/heater(Torrey Pines Scientific),a2151variable wavelength detector (LKB),and Chromeleon HPLC management software (Dionex).A linear acetonitrile-water gradient with0.1% (v/v)TFA(starting at34%(v/v)acetonitrile,increasing at1.3%/min)was used to elute the samples,at a total solvent flow rate of1mL/min.Absorbance was measured at280nm.The column temperature was20°C,and a sample volume of50µL was loaded.
Turbidity Measurements.Turbidity was monitored during refolding by diluting denatured lysozyme(0.63, 0.32,and0.16mg/mL)into a4mL cuvette containing refolding buffer.The denaturation and refolding condi-tions were the same as in the case of the10mL refolding experiments.The cuvette was covered,and the contents were briefly mixed.The cuvette was placed in a spectro-photometer,and the absorbance was monitored at600 nm for60min.
Fluorescence Measurements.The fluorescence spec-trum of native,denatured,and labeled lysozyme was measured using a luminescence spectrometer,LS50B (Perkin-Elmer).Excitation was at295nm with a slit width of2.5nm,and emission was monitored from305 to550nm at1200nm/min with a slit width of5nm. Refolding of Unlabeled Lysozyme.Denaturation and Reduction.Native lysozyme was denatured and reduced by incubating in denaturation buffer(8M GdmCl or8M urea,32mM DTT,50mM Tris,1mM EDTA,pH 8.0)for at least1h at37°C.The extent of denaturation was checked using RP-HPLC.The concentration of denatured lysozyme was measured by UV absorbance and varied between3and25mg/mL.
Refolding.Denatured and reduced lysozyme at a concentration of 3.5, 6.9,13.8,or21.6mg/mL was refolded by rapid dilution of665µL of denatured lysozyme into10mL of refolding buffer(5.33mM GSSG,50mM Tris,1mM EDTA,pH8.0,20°C)to give a final lysozyme concentration of0.22,0.43,0.86,or1.35mg/mL,respec-tively.The refolding solution was vortexed for30s and then left unstirred.Samples were collected at regular intervals and quenched immediately by adding30µL of 10%TFA to270µL of refold sample.Experiments were duplicated except for where the final lysozyme concentra-tion was1.35mg/mL,in which case the experiment was repeated in triplicate.
Kinetic Analysis.The kinetics of refolding was ana-lyzed in terms of a competing first-and third-order reaction scheme where refolding yield,y,is given by whereψ)(k2/k3U02)1/2,k2is the refolding rate constant, k3is the aggregation rate constant,and U0is the initial concentration of denatured protein in the refolding buffer at the start(6).The yield data obtained from the refolding experiments were used to estimate k2and k3based on an iterative least sum of squares fit to eq1.
y)ψ{tan-1[(1+ψ2)exp(2k
2
t)-1]1/2-tan-1ψ}(1)
Refolding with Labeled beling.Na-tive lysozyme was dissolved in bicarbonate buffer(0.1M sodium bicarbonate,pH8.6).The final concentration was 10.5mg‚mL-1.Approximately5mg of fluorescein isothio-cyanate(FITC)was dissolved in0.5mL of dimethyl sulfoxide(DMSO).A100µL aliquot of FITC solution was added to800µL of the native lysozyme solution while gently vortexing.The solution was left at room temper-ature for approximately1h.The labeled lysozyme was separated from the excess FITC using a Sephedex G25 gel filtration column(Amersham Pharmacia Biotech AB). The column was equilibrated with three column volumes of bicarbonate buffer.A0.5mL aliquot of labeled lysozyme solution was added to the top of the column. The column was eluted with1mL of bicarbonate buffer. The1mL fraction of labeled lysozyme was collected and the absorbance measured at280and494nm(absorbance maximum of FITC).The concentration of protein was calculated using
where A280is the absorbance at280nm,A494is the absorbance at494nm,CF is a correction factor given by CF)A280,free dye/A494,free dye,which for FITC has a value of 0.20,and lys is the extinction coefficient of native lysozyme at280nm(Molecular Probes).The concentra-tion of labeled lysozyme in the1mL eluted fraction was 0.73mg/mL.The degree of labeling,DOL,was calculated using
where MW is the molecular weight of the protein,C is the concentration of lysozyme calculated using eq2,and FITC is the extinction coefficient of FITC at494nm equal to68000cm-1‚M-1.The degree of labeling calculated using eq3was94%.The labeled lysozyme solution was analyzed using RP-HPLC and the enzymatic activity measured.
The labeling and separation procedure was repeated using a blank solution of bicarbonate buffer containing no lysozyme in order to ensure that no FITC was carried through the column during separation.This blank eluted fraction was used as a parallel control in subsequent refolding experiments.Both labeled lysozyme and blank control fractions were stored in darkness at4°C to minimize photobleaching of the label.
Refolding.Native lysozyme was denatured and re-duced as described previously.The refolding experiments were conducted using a method similar to that described previously,except that labeled lysozyme was added to the refolding buffer prior to the addition of unlabeled denatured-reduced lysozyme.The aim was to investigate whether labeled lysozyme could aggregate with the denatured-reduced lysozyme during dilution refolding. Refolding was initiated by rapidly diluting335µL of denatured-reduced lysozyme into5mL of renaturation buffer containing either6.8or13.5µg/mL of labeled lysozyme.Three different concentrations of denatured-reduced lysozyme were investigated giving final lysozyme concentrations in the renaturation buffer of0.8,0.4,and 0.2mg/mL,excluding the added labeled lysozyme present at either6.8or13.5µg/mL.The refolding yield was calculated on the basis of enzymatic assay and RP-HPLC analysis.The concentration of labeled lysozyme was subtracted from the final concentration of refolded lysozyme for the yield calculation.
Control experiments were conducted with unlabeled native lysozyme in the refolding buffer at the same concentrations as the experiments with labeled lysozyme and with the blank sample retained from the labeling process.The blank sample was used to confirm that excess free FITC was not carried through the gel filtra-tion column,thus contaminating the aggregates and thereby causing them to fluoresce.Additionally,labeled lysozyme(4.3mg/mL)was mixed with native lysozyme (8mg/mL)in equal proportions and with aggregates collected from a previous refolding experiment where no labeled lysozyme was present.This was done to test whether native and labeled lysozymes were stable in solution and to test whether labeled lysozyme could become incorporated into aggregates after refolding.Both samples were left for12h.
At the end of refolding,aggregates from each experi-ment were collected by resuspending the refolding solu-tion and taking a sample.The sample was centrifuged at1500g for5min and the supernatant decanted leaving the aggregates behind.The aggregates were resuspended in5mL of TE buffer(50mM Tris,1mM EDTA,pH8.0) by vortexing.Centrifugation and resuspension in fresh TE buffer was repeated a further two times,to remove free labeled lysozyme,and on final resuspension the aggregates were resuspended in1mL of TE buffer.Small drops of each washed aggregate suspension were trans-ferred using a micropipet to glass slides and covered with a glass cover slip.The aggregates were observed under a BX60microscope(Olympus)at40×magnification in both bright field mode and reflected light fluorescence mode using a superwide band filter set and a mercury vapor lamp(BX-FLA reflected light fluorescence attach-ment,Olympus).
Results and Discussion
Kinetics of Refolding and Aggregation.Figure2 shows the yield of native lysozyme for an experiment conducted at0.22mg/mL analyzed using enzymatic activity assay and RP-HPLC analysis.The enzymatic assay gave a higher yield of native lysozyme than the RP-HPLC method except at extended refolding time (>1000min).Figure3shows the chromatograms of the quenched refolding samples with time for the experi-ments reported in Figure2.The development of the native peak(N)with refolding time is clear.There is an
C)[A280-A494(CF)
lys](2)
DOL)A
494
MW
C
FITC
(3)
parison of the refolding yield based on enzymatic
activity assay and RP-HPLC analysis for0.22mg/mL lysozyme.
additional peak (M)that increases with time initially but is not present in the final sample taken beyond 1400min.Peak M may represent a misfolded conformation with incorrect disulfide bonds that undergoes disulfide rear-rangement to form the native structure after an extended time.On the basis of Figure 2,this misfolded conforma-tion appears to have some enzymatic activity.Previous analysis of lysozyme refolding kinetics has been based on enzymatic activity (6).For consistency,and since the misfolded conformation did not represent a permanent loss,yield in this study was determined by enzymatic activity.
The yield time course of lysozyme refolding at varying protein concentrations is shown in Figure 4.The yield of native lysozyme decreases significantly as concentration increases,as expected from eq 1.All data were quanti-tatively analyzed in terms of the kinetic model given by eq 1in order to obtain a single set of rate constants.For GdmCl denaturation the refolding and aggregation rate constants were 0.018min -1and 0.27mL 2‚mg -2‚min -1,respectively.The refolding and aggregation rate con-stants for the same conditions have previously been reported as 0.0450min -1and 0.728mL 2‚mg -2‚min -1(8).At high concentrations (>1mg/mL),where the yield is comparatively low (<40%),the model overestimates refolding yield.Industrial refolding operations often utilize urea in place of GdmCl as the denaturant for reasons of reduced toxicity,cost,and lower ionic strength,facilitating subsequent ion-exchange purification.A single set of refolding data was therefore collected with urea as the denaturant.The final concentration of lysozyme was 1.39mg/mL.The estimated refolding and aggrega-tion rate constants were ≈0.082min -1and ≈4.2mL 2‚mg -2‚min -1,respectively,which are significantly different from the rate constants for GdmCl denaturation.The kinetic model predicts that final yield at a fixed protein concentration is governed by the ratio of the refolding and aggregation rate constants (6),explaining quantita-tively why yield decreases when urea is used as the denaturant.
Turbidity data were collected during the refolding of GdmCl denatured lysozyme,at various concentrations.Figure 5shows the turbidity data and the yield of aggregated lysozyme calculated using the refolding and
aggregation rate constants estimated from Figure 4.The rate of increase in turbidity at 0.63mg/mL was signifi-cantly larger than at 0.32mg/mL.The rate of turbidity increase was slower than the estimated rate of aggrega-tion according to the kinetic model,and experimentally turbidity continued to increase after the model predicted a plateau.This reflects the fact that measured turbidity is not directly proportional to the concentration of ag-gregated lysozyme and that the kinetic description is simplistic.
Refolding with Labeled Lysozyme.FITC-labeled lysozyme was compared to native lysozyme using RP-HPLC,an enzymatic activity assay and fluorescence spectroscopy.The retention times in Figure 6a,b for native and denatured lysozyme (4.3and 7.2min,respec-tively)are significantly different and confirm that lysozyme was fully denatured prior to refolding.Chromatogram c in Figure 6shows a number of peaks in the labeled lysozyme sample,possibly reflecting varying degrees of labeling.The enzymatic activity of the labeled lysozyme was 60.7dA ‚dmin -1‚mg -1compared to 78.1dA ‚dmin -1‚mg -1for unlabeled native lysozyme.Binding of FITC to lysozyme therefore had a negative effect on enzymatic activity,and this may be due to some binding of FITC
to
Figure 3.Typical chromatograms of refolding samples at various times (data are for refolding at 0.22mg/mL).Peak N represents native lysozyme,and peak M represents a misfolded
species.
Figure 4.Refolding curves for GdmCl denatured-reduced lysozyme at various concentrations.The solid line is eq 1with k 2)0.018min -1and k 3)0.27mL 2‚mg -2‚min -1
.
Figure 5.Turbidity (600nm)versus time during refolding of lysozyme at various concentrations.The solid lines represent the concentration of aggregated lysozyme calculated using eq 1and a mass balance of lysozyme species (k 2)0.018min -1and k 3)0.27mL 2‚mg -2‚min -1)at the corresponding lysozyme concentrations.
the protein active site or to allosteric modulation of activity as a result of labeling.Figure 7shows the fluorescence spectrum of labeled lysozyme relative to native and denatured lysozyme.The spectrum of the labeled lysozyme is similar to the native spectrum except at higher wavelengths (525nm),where the emission of the bound FITC is visible.On the basis of these results it is reasonable to assert that labeled lysozyme has properties similar to native lysozyme and will behave similarly to native protein during refolding.However,we are unable to rule out some change in surface hydropho-bicity as a result of labeling.
To test whether substantially native lysozyme could be incorporated into the aggregates during refolding,FITC-labeled lysozyme was added to the refolding buffer prior to the addition of denatured lysozyme.The incor-poration of labeled lysozyme into aggregates during refolding would cause the aggregates to fluoresce when viewed in reflected light fluorescence mode.Figure 8shows the results of washed aggregates viewed in bright field and reflected light fluorescence mode.In both the unlabeled (A)and labeled (C)cases the aggregates can be clearly seen in bright field mode.However,in reflected light fluorescence mode (B and D)only aggregates from experiments where labeled lysozyme was present can be seen (D).This indicates that labeled lysozyme present in the refolding buffer prior to dilution was incorporated into the aggregates during the refolding process.
The amount of labeled lysozyme that was added to the refolding buffer was comparatively small compared to the amount of denatured lysozyme that was added during dilution (<7%).As such there was no significant effect on the observed refolding yield.It was not possible to quantify how much labeled lysozyme was incorporated into the aggregates on the basis of FITC absorbance at 494nm.This may be due to the absorbance of small aggregates that were not removed by centrifugation.The results of the control experiments confirmed that the fluorescence of the aggregates was not due to free FITC carried over from the labeling procedure.Addition-ally a mixture of labeled lysozyme and unlabeled native lysozyme did not aggregate at any observable rate.However,aggregates from refolding experiments where no labeled lysozyme was present were mixed with high concentrations of labeled lysozyme and the aggregates subsequently washed to remove the labeled lysozyme.
Aggregates treated in this fashion fluoresced,indicating that labeled lysozyme could be incorporated onto the surface of aggregates after the initial aggregation process.The existing kinetic model of lysozyme refolding and aggregation does not consider that native lysozyme formed during refolding,or present prior to refolding,can be incorporated into aggregates.However,our results unequivocally demonstrate that labeled lysozyme was incorporated into,or onto,aggregates during refolding.There are two possible pathways for native protein to become incorporated into aggregates,as indicated in Figure 1.On one hand,native protein may exist in equilibrium with an aggregating intermediate.Alterna-tively,native protein may aggregate by direct incorpora-tion into the aggregates,possibly involving some other intermediate.It is possible that this latter mechanism involves,at least to some extent,an equilibrium exchange between the bulk and the aggregates.This possibility is supported by reports that the early stages of aggregation have been shown to be reversible (9,10).On the basis of these results it is not possible to determine what the mechanism of incorporation is.However,the
existing
Figure 6.Chromatograms of native lysozyme (a,59µg/mL in TE buffer),denatured-reduced lysozyme (b,126µg/mL in 0.1M acetic acid),and labeled native lysozyme (c,14µg/mL in bicarbonate
buffer).
Figure 7.Fluorescence spectrum of native,denatured,and labeled lysozyme with excitation at 295
nm.
Figure 8.Washed aggregates from refolding experiments under bright field (A,C)and reflected light fluorescence mode (B,D)at 40×magnification.Plates A (bright field mode)and B (fluorescence mode)show the typical view of aggregates obtained when no labeled protein was present in the renaturation buffer.Plates C (bright field mode)and D (fluorescence mode)show the typical view of aggregates obtained when FITC-labeled lysozyme was present in the renaturation buffer prior to dilution.
kinetic model will clearly overpredict yield if used in standard reactor design equations,since the inclusion of a back-reaction can drastically alter the optimal operat-ing strategy(3,4).This is particularly true for fed-batch operation.Subsequent work will seek to define an alternative kinetic scheme that is generally applicable and,therefore,independent of the chosen reactor con-figuration and operational strategy.
Conclusions
A set of rate constants was obtained from the refolding data at varying concentrations assuming that first-order refolding competes with third-order aggregation(6),and these rate constants were the same order of magnitude as those reportedly previously(8).The corresponding rate constants for urea denaturation were also estimated,and the refolding rate constant increased approximately4×, whereas the aggregation rate constant increased ap-proximately10×.The relative differences in the rate constants for GdmCl and urea explains,in a kinetic sense,why refolding yield is lower for urea-denatured lysozyme.
Native lysozyme was successfully labeled with FITC. The labeled lysozyme retained most of its activity,and the fluorescence spectrum was similar to that of native lysozyme.The labeled lysozyme was added to refolding experiments and was clearly incorporated into aggregates during refolding.This provides evidence for a back-reaction of native protein to aggregates during refolding, either via an intermediate or by direct surface incorpora-tion onto the aggregates.The current kinetic model does not allow for an incorporation of native lysozyme into aggregates,and this may explain why the model over-estimates yield at high protein concentration(>1mg/ mL).Loss of native protein to aggregates can significantly affect the optimization of refolding operations,and neglect of this pathway can lead to the design of a suboptimal process,as demonstrated analytically for fed-batch and continuous refolding reactors(3,4).
References and Notes
(1)Zettlmeissl,G.;Rudolph,R.;Jaenicke,R.Reconstitution of
Lactic Dehydrogenase.Noncovalent Aggregation vs Reactiva-tion. 1.Physical Properties and Kinetics of Aggregation.
Biochemistry1979,18,5567-5571.
(2)Goldberg,M.E.;Rudolph,R.;Jaenicke,R.A Kinetic Study
of the Competition between Renaturation and Aggregation during the Refolding of Denatured Reduced Egg-White Lysozyme.Biochemistry1991,30,2790-2797.
(3)Middelberg,A.P.J.The Influence of Protein Refolding
Strategy on Cost for Competing Reactions.Chem.Eng.J.
1996,61,41-52.
(4)Kotlarski,N.;O’Neill,B.K.;Francis,G.L.;Middelberg,A.
P.J.Design Analysis for Refolding Monomeric Protein.
AIChE J.1997,43,2123-2132.
(5)Kiefhaber,T.;Rudolph,R.;Kohler,H.H.;Buchner,J.
Protein Aggregation In vitro and In vivo-A Quantitative Model of the Kinetic Competition between Folding and Aggregation.Bio/Technology1991,9,825-829.
(6)Hevehan,D.L.;De Bernardez Clark,E.Oxidative Rena-
turation of Lysozyme at High Concentrations.Biotechnol.
Bioeng.1997,54,221-230.
(7)Saxena,V.P.;Wetlaufer, D. B.Formation of Three-
Dimensional Structure in Proteins.I.Rapid Nonenzymic Reactivation of Reduced Lysozyme.Biochemistry1970,9, 5015-5022.
(8)Maachupalli-Reddy,J.;Kelley,B.D.;Clark,E.D.Effect of
Inclusion Body Contaminants on the Oxidative Renaturation of Hen Egg White Lysozyme.Biotechnol.Prog.1997,13,144-150.
(9)Cleland,J.L.;Wang,D.I.C.Refolding and Aggregation of
Bovine Carbonic Anhydrase-B s Quasi-Elastic Light-Scatter-ing Analysis.Biochemistry1990,29,11072-11078.
(10)Cleland,J.L.;Wang,D.I.C.Equilibrium Association of a
Molten Globule Intermediate in the Refolding of Bovine Carbonic-Anhydrase.ACS Symp.Ser.1991,470,169-179. Accepted for publication February20,2002.
BP0200189。