A New Kinetic Scheme for Lysozyme
`Refolding and Aggregation
`
`A. Mark Buswell, Anton P. J. Middelberg
`
`Department of Chemical Engineering, University of Cambridge, Pembroke
`Street, Cambridge CB2 3RA United Kingdom; telephone: +44 1223 334 777;
`fax: +44 1223 334 796; e-mail: antonm@cheng.cam.ac.uk
`
`Received 8 November 2002; accepted 3 March 2003
`
`DOI: 10.1002/bit.10705
`
`Abstract: The competing first- and third-order reaction
`scheme for lysozyme is shown to not predict fed-batch
`lysozyme refolding when the model is parameterized us-
`ing independent batch experiments, even when varia-
`tions in chemical composition during the fed-batch ex-
`periment are accounted for. A new kinetic scheme is pro-
`posed that involves rapid partitioning between the
`alternative fates of refolding and aggregation, and which
`allows for aggregation via a sequential mechanism. The
`model assumes that monomeric lysozyme in different
`states, including native, is able to aggregate with inter-
`mediates, accounting for recent experimental evidence
`that native protein can be incorporated into aggregates
`and explaining why native protein in the refolding buffer
`reduces yield. Stopped-flow light-scattering measure-
`ments were used to measure the association rate for the
`sequential aggregation mechanism, and refolding rate
`constants were determined in a series of batch experi-
`ments designed to be “snapshots” of the composition
`during a fed-batch experiment. The new kinetic scheme
`gave a good a priori prediction of fed-batch refolding
`performance. © 2003 Wiley Periodicals, Inc. Biotechnol Bioeng
`83: 567–577, 2003.
`Keywords: lysozyme; refolding; aggregation; protein;
`kinetics
`
`INTRODUCTION
`Inclusion bodies are aggregates of protein that contain a
`high proportion of the target protein, typically 50% by mass,
`which can be recovered with relative ease following cell
`disruption (Kane and Hartley, 1988; Middelberg and
`O’Neill, 1998). Subsequent processing of these recovered
`inclusion bodies typically involves solubilization using con-
`centrated denaturant supplemented with reducing agent,
`oxidative refolding, and chromatographic purification
`(Thatcher, 1990). Of these process steps, oxidative refold-
`ing is often the yield bottleneck and is difficult to optimize
`and scale due to a lack of rigorous models. The most eco-
`nomic and simplest refolding method, termed dilution re-
`folding, involves dilution of the denatured-reduced protein
`into a refolding buffer of optimized chemical composition.
`A disadvantage of dilution is that the yield of native protein
`is often low due to the aggregation of partially folded in-
`termediates. It is nevertheless frequently employed as over-
`all process cost and complexity usually increase when more
`complicated methods are used.
`
`© 2003 Wiley Periodicals, Inc.
`
`Batch dilution is often used in laboratory refolding stud-
`ies, and simplified kinetic schemes have been developed to
`describe the yield of native product based on the assumption
`that first-order refolding competes with higher-order aggre-
`gation (Kiefhaber et al., 1991). These schemes have been
`used to describe the refolding yield of human carbonic an-
`hydrase B by diafiltration and lysozyme by dilution (Heve-
`han and De Bernardez Clark, 1997; Vicik and De Bernardez
`Clark, 1991). In all cases, protein aggregation is modeled
`empirically as a reaction of variable order, allowing the
`model to fit experimental data through three regressed pa-
`rameters (two rate constants and the order of the aggrega-
`tion reaction). For example, refolding yield of lysozyme is
`most accurately described by assuming a third-order aggre-
`gation reaction (Hevehan and De Bernardez Clark, 1997).
`There have been no attempts to interpret such empirical
`higher-order dependencies in terms of a mechanistic under-
`standing of the aggregation process, except to suggest that
`the gross aggregation process is more complex than a
`simple second-order dimerization step. In general, the re-
`sulting kinetic schemes require careful validation before
`their use in alternative reactor topographies.
`Reactor design theory predicts that batch refolding will
`not be optimal when the objective is to maximize the se-
`lectivity for a product formed by first-order refolding in
`competition with higher-order aggregation. Fed-batch re-
`folding strategies have therefore been developed that com-
`bat aggregation by controling the rate of denatured protein
`addition into the refolding buffer, thereby minimizing the
`concentration of aggregating intermediates (Fischer et al.,
`1992; Katoh et al., 1997; Phue et al., 2000). A comparative
`study using numerical simulation of economic efficiency for
`batch, fed-batch, and continuous refolding strategies
`showed that batch refolding is likely to be more than twice
`as expensive as either fed-batch or continuous modes (Kot-
`larski et al., 1997). Conclusions from these numerical stud-
`ies are, however, very sensitive to the assumed kinetic
`scheme. For example, process cost increases enormously
`when a backward reaction, from native to aggregate, is in-
`troduced to the competing first- and second-order reaction
`pathway (Middelberg, 1996). Such a backward reaction has
`little effect in batch studies, where the predominant reaction
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`pathway is to deplete denatured protein, but becomes sig-
`nificant in fed-batch or continuous formats where the re-
`folding buffer may contain a substantial amount of folded
`protein. The involvement of native protein in the aggrega-
`tion pathway appears plausible through two mechanisms. In
`the first, native protein may exist in equilibrium with inter-
`mediate, thereby providing a reverse pathway for native
`protein to aggregate. Second, native protein may aggregate
`directly during the dilution of fully denatured protein into
`the refolding buffer. Recently, the existence of a backward
`pathway has been demonstrated experimentally for lyso-
`zyme using fluorescent labeling techniques (Buswell and
`Middelberg, 2002).
`It is clear that the prediction of refolding yield in a given
`reactor format requires knowledge of the simplest correct
`kinetic scheme. A kinetic scheme that is only applicable to
`the reactor format used to establish it is of no fundamental
`value. However, to date, there are no detailed studies that
`critically assess simple batch-derived models in alternative
`reactor formats (e.g., fed-batch) through combined numeri-
`cal and experimental studies. This study therefore seeks to
`establish whether or not the standard first- and higher-order
`competing reaction scheme (Fig. 1), established in batch
`reactor systems, can be used in other reactor formats. This
`is done through combined simulation and experimental
`studies. Importantly, we recognize that the chemical com-
`position of the buffer changes throughout the fed-batch re-
`folding process. The model is therefore parameterized in a
`series of batch-tests that are “snapshots” of the fed-batch
`composition. Despite accounting for this variation, we con-
`clusively show that the existing first- and third-order
`scheme for lysozyme refolding, derived by batch studies,
`cannot be applied to predict yield in fed-batch refolding.
`This is expected based on our recent finding that native
`protein can be incorporated into aggregates (Buswell and
`Middelberg, 2002). A new kinetic scheme, shown in Figure
`2, is proposed and used to make a good a priori prediction
`of fed-batch refolding yield.
`
`EXPERIMENTAL METHODS
`
`The concentrations of native and of denatured-reduced ly-
`sozyme were calculated based on absorbance at 280 nm
`using extinction coefficients of 2.63 or 2.37 mL mg−1 cm−1,
`respectively (Saxena and Wetlaufer, 1970). Native lyso-
`
`Figure 1.
`Simplified kinetic scheme showing first-order refolding com-
`peting with higher-order aggregation, where kr is the refolding rate con-
`stant and ka is the aggregation rate constant (Hevehan and De Bernardez
`Clark, 1997).
`
`Figure 2. Refolding and aggregation scheme with initial partitioning
`between refolding and aggregation. The aggregation mechanism involves
`sequential polymerization. Intermediates committed to refolding and native
`protein can aggregate with noncommitted intermediates only. kcr is the rate
`of commitment to refolding, kr is the rate limiting refolding rate and kas is
`the association rate constant for sequential aggregation.
`
`zyme samples were diluted in the same buffer as they were
`originally prepared in. Denatured lysozyme samples were
`diluted into 0.1M acetic acid.
`Native lysozyme was denatured and reduced by incuba-
`tion in denaturation buffer (8M urea, 32 mM DTT, 50 mM
`Tris, 1 mM EDTA, pH 8.0) for at least 1 h at 37°C. Com-
`plete denaturation was confirmed using RP-HPLC. The
`concentration of denatured lysozyme was measured by UV
`absorbance.
`The enzymatic activity of samples from the refolding
`experiments was measured at ambient temperature by fol-
`lowing the decrease in absorbance at 450 nm of a cell sus-
`pension (0.15 mg/mL−1Micrococcus lysodeikticus (Sigma),
`0.067M sodium phosphate, pH 6). Samples were collected
`during the refolding experiments at various intervals and
`quenched to arrest the refolding reaction by adding 30 ␮L of
`10% TFA to 270 ␮L of sample. The samples were further
`diluted with acidified TE buffer (1% TFA, 50 mM Tris, 1
`mM EDTA) to give a total protein concentration of 0.1 mg
`mL−1. Twenty microliters of the diluted sample was added
`to 980 ␮L of cell suspension, giving a total protein concen-
`tration of 2 ␮g mL−1, and was briefly mixed. After 5 s the
`absorbance was monitored for 30 s. A linear decrease in
`aborbance was observed. The percentage of native protein
`was calculated as the ratio of the slope of the absorbance
`decay of the sample to the slope obtained for a native ly-
`sozyme standard.
`
`Kinetics Using a Competing First- and
`Third-Order Scheme
`A typical fed-batch refolding strategy was considered which
`corresponded to denatured protein solution (8M urea, 32
`mM DTT, 50 mM Tris, 1 mM EDTA, pH 8.0) being fed into
`140 mL of refolding buffer (4 mM GSSG, 50 mM Tris, 1
`mM EDTA, pH 8.0) at 0.083 mL min−1 for 120 min. Since
`
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`the difficulty of preparing denatured and reduced lysozyme
`at 38 mg/mL−1 and higher. The end-point yield data at vary-
`ing final protein concentrations was used to estimate ka
`based on the solution to the competing first- and third-order
`scheme, where the refolding rate constants, kr, were fixed at
`the values estimated from the experiments at low protein
`concentration (0.025 and 0.05mg/mL−1) (Hevehan and De
`Bernardez Clark, 1997).
`
`Fed-Batch Refolding Experiment
`
`Fed-batch refolding was conducted in a simple baffled
`stirred reaction vessel (Buswell et al., 2002). Urea-
`denatured lysozyme (13.4 mg/mL−1, 8M urea, 32 mM DTT,
`50 mM Tris, 1 mM EDTA, pH 8, ≈ 20°C) was fed at 0.083
`mL/min−1 into the reaction vessel, which contained 140 mL
`of refolding buffer (4 mM GSSG, 50 mM Tris, 1 mM
`EDTA, pH 8, ≈ 20°C), for 120 min using a peristaltic pump
`(Watson Marlow 101 U/R). The final lysozyme concentra-
`tion was 0.96 mg/mL−1. The solution was mixed continu-
`ously by the impeller rotating at 350 rpm. Upon completion
`of feeding (after 120 min), the solution was left for 30 min
`with agitation. Samples (270 ␮L) were collected every 10
`min and quenched immediately by adding 30 ␮L of 10%
`TFA to 270 ␮L of refold sample. One final sample was
`collected after more than approximately 8 h. Samples were
`analyzed for enzymatic activity.
`
`Simulation Using a Competing First- and
`Third-Order Scheme
`
`The rate constant data in Table II were regressed to empiri-
`cal relationships where the independent variable was the
`volume of denatured solution added during the fed-batch
`experiment, Va. The resulting equations are:
`
`= 0.0171 +
`
`kr
`
`,
`
`ka
`
`0.162
`共1 + e关共Va−4.83兲Ⲑ0.977兴兲
`= 7.92 − 0.400 ⭈ Va.
`The relationships do not have a physical significance and
`were solely for modeling convenience. The concentration of
`the three protein species shown in Figure 1, and the volume
`
`(1)
`
`(2)
`
`the concentrations of urea and DTT change continually dur-
`ing fed-batch refolding, various “snapshot” conditions ap-
`plicable to the process were selected to quantify refolding
`and aggregation kinetics. The values chosen are shown in
`Table I.
`Refolding was initiated by diluting a specific volume of
`denatured and reduced lysozyme at a specific initial con-
`centration into 3 mL of refolding buffer (4 mM GSSG, 50
`mM Tris, 1 mM EDTA, pH 8.0, ≈ 20°C). The volume of
`denatured-reduced lysozyme diluted into the refolding
`buffer was varied to enable investigation of different chemi-
`cal compositions. The refolding solution was vortexed for
`10 s and then left unstirred. For experiments to determine
`the refolding rate, samples were collected at regular inter-
`vals (2, 4, 8, 16, 32, 64, 128, and 1000 min) and quenched
`immediately by adding 30 ␮L of 10% TFA to 270 ␮L of
`refolding sample. For experiments to determine the aggre-
`gation rate, a single sample was collected after ≈ 1000 min.
`These samples were not quenched with TFA prior to analy-
`sis. All samples were analyzed by enzymatic activity. Each
`refolding experiment for the determination of rate constants
`was conducted in triplicate.
`The rate constant of the first-order refolding reaction was
`measured by monitoring the yield of native lysozyme with
`time. Two final concentrations of lysozyme (0.025 mg
`mL−1and 0.05 mg mL−1) were used. These two low con-
`centrations were used to confirm that no significant aggre-
`gation occurred and that there was no dependence of yield
`on final protein concentration. The refolding rate constant,
`kr, was estimated for each chemical composition by regres-
`sion to a standard first-order rate law.
`The aggregation reaction order was fixed as third-order
`(Hevehan and De Bernardez Clark, 1997). Refolding ex-
`periments were conducted at higher final lysozyme concen-
`trations to calculate the aggregation rate constants using the
`same chemical concentrations defined in Table I. The final
`lysozyme concentrations investigated were 0.025, 0.05, 0.1,
`0.2, 0.4, and 0.8 mg/mL−1. For some of the initial chemical
`compositions shown in Table I it was not possible to mea-
`sure aggregation at the highest overall concentrations due to
`
`Table I. Concentrations of urea, DTT, and GSSG used to investigate
`refolding and aggregation kinetics. The values correspond so those that
`would occur during a fed-batch refolding strategy where denatured protein
`solution (8M urea, 32 mM DTT, 50 mM Tris, 1 mM EDTA, pH 8.0) is fed
`into 140 mL of refolding buffer (4 mM GSSG, 50 mM Tris, 1 mM EDTA,
`pH 8.0) at 0.083 mL min−1 for 120 min. The volumes shown in the first
`column were those added to 3 mL of refolding buffer.
`
`Table II. Refolding (kr) and aggregation (ka) rate constants at various
`dilution ratios.
`
`Volume of denatured
`lysozyme solution
`(␮L)
`
`Concentration
`of urea
`(M)
`
`Concentration
`of DTT
`(mM)
`
`Concentration
`of GSSG
`(mM)
`
`Concentration
`of urea
`(M)
`
`Concentration
`of DTT
`(mM)
`
`kr
`(min−1)
`
`ka
`(mL2 mg−2 min−1)
`
`33
`69
`102
`141
`177
`213
`
`0.09
`0.18
`0.26
`0.36
`0.45
`0.53
`
`0.35
`0.72
`1.05
`1.44
`1.78
`2.12
`
`3.95
`3.91
`3.86
`3.82
`3.78
`3.73
`
`0.09
`0.18
`0.26
`0.36
`0.45
`0.53
`
`0.35
`0.72
`1.05
`1.44
`1.78
`2.12
`
`0.022
`0.044
`0.095
`0.155
`0.179
`0.175
`
`8.10
`5.99
`4.74
`6.55
`4.65
`3.79
`
`BUSWELL AND MIDDELBERG: A NEW KINETIC SCHEME FOR LYSOZYME REFOLDING AND AGGREGATION
`
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`of the reactor were described by the following differential
`equations,
`
`dI
`dt
`
`=− krI − kaI3 + F
`V
`
`− I兲
`
`共Ii
`
`N
`
`= krI − F
`V
`= kaI3 − F
`V
`
`A
`
`= F,
`
`dN
`dt
`
`dA
`dt
`
`dV
`dt
`
`with initial conditions,
`I共0兲 = N共0兲 = A共0兲 = 0,
`
`and,
`
`(3)
`
`(4)
`
`(5)
`V共0兲 = 140 mL,
`where F is the feed rate of denatured protein solution, Ii is
`the concentration of denatured protein, and V is the volume
`of solution in the reactor. The differential equations shown
`in Eq. (3) were solved using PolyMath Version 5.01
`(CACHE Corp., www.polymath-software.com).
`
`Batch Refolding With Native Lysozyme Present
`
`Batch dilution experiments were conducted where the re-
`folding buffer contained varying concentrations of native
`lysozyme before dilution. Refolding was initiated by dilut-
`ing denatured and reduced lysozyme at specific initial con-
`centrations into 3 mL of refolding buffer, which contained
`native lysozyme (5.33 mM GSSG, 50 mM Tris, 1 mM
`EDTA, pH 8.0, ≈ 20°C). The dilution volumes and resulting
`chemical compositions are shown in Table III. The concen-
`trations of protein are shown in Table IV. The initial con-
`centrations of native lysozyme were selected based on typi-
`cal concentrations that are likely to occur during fed-batch
`refolding. The refolding solution was vortexed for 10 s and
`then left stagnant. A single sample for each dilution experi-
`ment was collected after ≈ 16 h. The samples were not
`quenched with TFA prior to analysis. Each sample was
`analyzed, in triplicate, by enzymatic activity. Each refolding
`experiment was conducted in triplicate. The effective re-
`folding yield was calculated according to Eq. (6):
`
`Table III. Description of dilution factors and final urea, DTT, and GSSG
`concentrations. The concentration of DTT and GSSG do not take into
`account the effect of the redox equilibrium.
`
`Vol denatured solution
`added to 3 mL of
`refolding buffer
`(mL)
`
`Final urea
`concentration
`(M)
`
`Final DTT
`concentration
`(mM)
`
`Final GSSG
`concentration
`(mM)
`
`0.22
`0.14
`
`0.53
`0.36
`
`2.12
`1.44
`
`3.73
`3.82
`
`⭈ Vini
`
`,
`
`(6)
`
`Yieldeffective
`
`= Cfinal
`
`− Cini
`⭈ Vfinal
`⭈ Vden
`Cden
`where Cfinal is the final concentration of native lysozyme,
`Cden is the concentration of the denatured lysozyme added
`during the dilution, Cini is the initial concentration in the
`refolding buffer prior to dilution, Vfinal is the final concen-
`tration after dilution, Vden is the volume of denatured solu-
`tion added during dilution, and Vini is the initial volume of
`refolding buffer before dilution.
`
`Measurement of Aggregation Rate Using Classic
`Light Scattering, kas
`The rate of aggregation was measured using classic light
`scattering. A sequential aggregation model was used to
`simulate the transient size distribution of aggregates, which
`enabled a simulated light-scattering signal to be regressed to
`the measured light-scattering signals, thus estimating the
`association rate constant for aggregation. The 90° stopped
`flow light-scattering experiments were conducted on a
`PiStar-180 Circular Dichroism Spectrometer (Applied Pho-
`tophysics, UK). The set-up of the machine was adjusted so
`that the emission signal could be monitored at the same
`wavelength as excitation, at 90° from the incident path. The
`excitation and emission slit widths were 2 nm and the path
`length was 10 mm. The stopped-flow mixing assembly was
`reported to have a dead time of 1 ms. The loading syringes
`for the stopped-flow apparatus dispensed solution in a vol-
`ume ratio of 1:10. To maintain consistent final buffer com-
`positions the fully denatured lysozyme solution (8M urea,
`32 mM DTT, 50 mM Tris-HCl, 1 mM EDTA, pH 8.0, 20°C)
`was diluted just prior to loading into the syringes by adding
`450 ␮L of renaturation buffer (5.33 mM GSSG, 50 mM
`Tris-HCl, 1 mM EDTA, pH 8.0, 20°C) to 1 mL of the
`denatured lysozyme solution. This dilution results in a urea
`concentration of 5.5M and a DTT concentration of 5.8 mM,
`which were confirmed sufficient to maintain the denatured
`state of the protein by turbidity and fluorescence measure-
`ments. The diluted denatured lysozyme solutions and re-
`folding buffer (5.33 mM GSSG, 50 mM Tris-HCl, 1 mM
`EDTA, pH 8.0, 20°C) were loaded into syringes having a
`volume ratio of 1:10, respectively. Based on the range of
`initial denatured lysozyme concentrations used the final ly-
`sozyme concentrations ranged between 0.09 mg mL−1 and
`0.75 mg mL−1. The signal was monitored for 20 s and was
`the average of eight repeat measurements.
`Rayleigh light-scattering theory predicts that the light-
`scattering signal will be proportional to the sum of the
`square of the molecular weight multiplied by the corre-
`sponding number concentration for the range of species
`present in the solution, i.e.,
`⬀ 兺 Mi2 Ai,
`
`where Ai is the number concentration of component i (Dol-
`linger et al., 1992). The relationship is subject to the under-
`lying assumptions of the derivation. These assumptions are
`
`(7)
`
`Is
`
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`Table IV. Refolding yields for batch refolding experiments with native protein included in the
`initial refolding buffer.
`
`Chemical
`composition
`
`Denatured lysozyme
`concentration
`(mg mL−1)
`
`Initial native
`concentration
`(mg mL−1)
`
`Total lysozyme
`concentration
`after dilution
`(mg mL−1)
`
`Effective refolding
`yield of denatured
`lysozyme
`(%)
`
`76 ± 10
`47 ± 3
`24 ± 4
`42 ± 2
`34 ± 3
`30 ± 9
`
`73 ± 2
`54 ± 4
`41 ± 4
`50 ± 3
`44 ± 1
`37 ± 3
`
`0.22
`0.48
`0.75
`0.44
`0.69
`0.97
`
`0.15
`0.40
`0.67
`0.29
`0.55
`0.82
`
`0 0
`
`.25
`0.53
`
`0 0
`
`.25
`0.53
`
`0 0
`
`.25
`0.53
`
`0 0
`
`.25
`0.53
`
`[urea] ⳱ 0.53M
`[DTT] ⳱ 2.12 mM
`[GSSG] ⳱ 3.73 mM
`
`[urea] ⳱ 0.36M
`[DTT] ⳱ 1.44 mM
`[GSSG] ⳱ 3.82 mM
`
`3.32
`
`6.56
`
`3.32
`
`6.56
`
`that the scatterers are small relative to the wavelength of the
`incident light, the concentration of scattering species is low
`so that the virial expansions can be ignored, and that the
`refractive index increment is constant over the range of
`concentrations investigated. Therefore, from Eq. (7), the
`transient size distribution of aggregates is required, which
`requires a detailed aggregation mechanism. The aggregation
`process was modeled using a sequential aggregation mecha-
`nism. Sequential polymerization involves the addition of
`monomeric subunits to a growing aggregate (Fig. 5). This
`mechanism is common for biological systems like actin po-
`lymerization (Tobacman and Korn, 1983) and amyloid fibril
`formation (Jarrett and Lansbury, 1992). Sequential poly-
`merization was described using a set of ordinary differential
`equations for the formation of native protein, the formation
`of aggregates, and the depletion of intermediate protein,
`
`dN
`dt
`
`= kcrI,
`
`dA2
`dt
`
`= 1
`2
`
`kasI2 − kasIA1,
`
`dAi
`dt
`
`dI
`dt
`
`= kasIAi−1
`
`− kasIAi,
`
`=− kcrI − kasI2 − kasI 兺
`
`19
`
`i=2
`
`(8)
`
`(9)
`
`(10)
`
`(11)
`
`Ai,
`
`where I and N are the number concentrations of intermedi-
`ate and native lysozyme, Ai is the number concentration of
`aggregates made up of i-mers, kcr is the commitment to
`refolding rate constant, kas is the association rate constant
`and t is time. To constrain the numerical complexity of the
`calculations a maximum aggregate size of 20-mers was con-
`sidered and the aggregation rate constant was assumed the
`same for all aggregation reactions (Speed et al., 1997).
`
`Estimation of Commitment to Refolding Rate, kcr
`The essential feature of the kinetic scheme shown in Figure
`2 is the initial partition between intermediates committed
`toward refolding and aggregation. This type of kinetic
`scheme has been proposed for carbonic anhydrase B (Cle-
`land and Wang, 1990; Vicik and De Bernardez Clark, 1991)
`and experimental data have indicated that early partitioning
`does occur in the case of lysozyme (Goldberg et al., 1991).
`The yield vs. concentration profile is governed by the ratio
`of the association rate constant, kas, and the first-order rate
`constant for commitment to refolding, kcr. By regression to
`the experimental yield vs. concentration data obtained in the
`batch experiments, the ratio of the association rate constant
`and the rate constant for commitment to refolding, kas/kcr,
`was estimated for the various chemical compositions. kcr is
`then uniquely determined for a given chemical composition
`as kas is known from the stopped-flow experiments.
`
`Simulation of Fed-Batch Refolding Using New
`Kinetic Scheme
`
`To simulate fed-batch refolding, the rate constants for the
`new kinetic scheme are required over the range of chemical
`compositions that occur during the fed-batch process. The
`ratio of the association and commitment rate constants for
`the different chemical compositions was estimated from the
`yield vs. concentration data as already described. The com-
`mitment rate constants were estimated by fixing the asso-
`ciation rate constant to the value estimated from the light-
`scattering measurements conducted at the final chemical
`composition (0.53M urea, 2.12 mM DTT, 3.73 mM GSSG).
`The limiting refolding rate, kr, was the same as the mea-
`sured first-order rate obtained from the batch experiments
`(Table I). The new kinetic scheme shown in Figure 2 was
`used to define fed-batch reactor equations. The design and
`operational parameters of the fed-batch reactor were the
`same as already described.
`
`BUSWELL AND MIDDELBERG: A NEW KINETIC SCHEME FOR LYSOZYME REFOLDING AND AGGREGATION
`
`571
`
`Page 5
`
`

`

`Table V. Batch refolding data at low lysozyme concentrations (where no aggregation is assumed to occur) with time and varying chemical composition.
`
`Chemical composition
`
`[urea] ⳱ 0.09M, [DTT] ⳱ 0.35 mM
`
`[urea] ⳱ 0.18M, [DTT] ⳱ 0.72 mM
`
`[urea] ⳱ 0.26M, [DTT] ⳱ 1.05 mM
`
`Total concentration of refolding lysozyme (mg mL−1)
`
`0.023
`
`0.043
`
`0.021
`
`0.047
`
`0.022
`
`0.043
`
`Yield
`(%)
`
`13.8
`16.7
`19.5
`27.3
`40.9
`51.1
`51.7
`84.0
`
`SD
`
`1.4
`1.8
`2.4
`1.5
`0.6
`1.2
`9.7
`4.7
`
`Yield
`(%)
`
`12.0
`15.3
`22.2
`30.8
`44.7
`58.5
`66.2
`79.2
`
`SD
`
`2.9
`3.8
`4.1
`5.8
`5.5
`7.6
`8.4
`8.6
`
`Yield
`(%)
`
`16.6
`26.7
`36.2
`39.7
`45.8
`60.7
`59.5
`74.2
`
`SD
`
`1.9
`3.9
`6.1
`9.0
`10.9
`10.3
`12.7
`5.6
`
`Yield
`(%)
`
`14.7
`21.3
`31.9
`43.0
`55.9
`68.9
`68.5
`75.6
`
`SD
`
`0.5
`1.0
`1.4
`1.7
`8.3
`5.5
`8.3
`4.7
`
`Yield
`(%)
`
`20.1
`32.5
`46.8
`62.1
`69.5
`78.8
`76.8
`75.2
`
`SD
`
`0.9
`4.9
`3.5
`8.7
`5.9
`3.8
`7.3
`16.8
`
`Yield
`(%)
`
`18.4
`28.8
`41.7
`52.5
`64.9
`74.6
`72.8
`72.7
`
`SD
`
`1.7
`1.4
`3.6
`6.7
`4.1
`7.9
`6.7
`8.0
`
`Chemical composition
`
`[urea] ⳱ 0.36M, [DTT] ⳱ 1.44 mM
`
`[urea] ⳱ 0.45M, [DTT] ⳱ 1.78 mM
`
`[urea] ⳱ 0.53M, [DTT] ⳱ 2.12 mM
`
`Total concentration of refolding lysozyme (mg mL−1)
`
`0.021
`
`0.042
`
`0.022
`
`0.045
`
`0.022
`
`0.044
`
`SD
`
`Yield
`(%)
`
`SD
`
`Yield
`(%)
`
`SD
`
`Yield
`(%)
`
`SD
`
`Yield
`(%)
`
`SD
`
`Time
`(min)
`
`2
`4
`8
`16
`32
`64
`128
`1000
`
`Time
`(min)
`
`Yield
`(%)
`
`22.6
`36.6
`57.3
`68.5
`77.5
`77.9
`75.3
`77.8
`
`2
`4
`8
`16
`32
`64
`128
`1000
`
`SD
`
`1.4
`3.8
`4.2
`4.6
`2.2
`7.7
`4.5
`10.3
`
`Yield
`(%)
`
`22.5
`36.8
`55.6
`74.0
`88.6
`83.0
`85.6
`83.7
`
`RESULTS AND DISCUSSION
`
`2.5
`2.2
`3.7
`3.6
`1.9
`3.9
`2.8
`3.8
`
`23.4
`39.0
`60.8
`78.3
`86.9
`75.0
`79.1
`86.5
`
`1.9
`1.9
`3.4
`5.7
`7.7
`4.2
`5.2
`6.5
`
`24.4
`39.1
`61.4
`75.7
`95.8
`85.2
`87.5
`83.9
`
`1.4
`0.8
`1.0
`2.8
`6.4
`3.4
`5.6
`1.1
`
`22.0
`38.4
`65.9
`72.9
`75.4
`83.7
`79.8
`82.9
`
`5.0
`7.4
`7.5
`9.9
`10.6
`6.3
`11.7
`14.1
`
`23.8
`38.6
`59.7
`75.0
`80.5
`82.9
`77.8
`81.2
`
`2.3
`2.7
`4.0
`5.4
`1.9
`4.7
`5.5
`4.7
`
`Evaluation of Competing First- and
`Third-Order Kinetics
`
`The batch refolding data at low lysozyme concentrations
`and varying times for different chemical compositions is
`given in Table V, and the final batch refolding yield data at
`various lysozyme concentrations and chemical composi-
`tions is given in Table VI. The refolding rate experiments at
`
`low lysozyme concentration showed good agreement with a
`first-order rate law under all chemicals compositions inves-
`tigated. To illustrate this, Figure 3 shows the regression fit
`of the first-order rate law to the refolding data at one of the
`chemical compositions. There was no dependence of refold-
`ing rate or final yield on lysozyme concentration, suggest-
`ing that aggregation was insignificant at these low concen-
`trations. However, the final yield at each dilution was 80%
`and did not reach 100% even at these low protein concen-
`trations. This has been reported before and it may be that
`
`Table VI. Final batch refolding yield at varying total lysozyme concentrations and varying chemical compositions.
`
`Final concentrations (mg mL−1)
`
`0.025
`
`0.05
`
`0.1
`
`0.2
`
`0.4
`
`0.8
`
`[urea]
`(M)
`
`[DTT]
`(mM)
`
`0.09
`0.18
`0.26
`0.36
`0.45
`0.53
`
`0.35
`0.72
`1.05
`1.44
`1.78
`2.12
`
`Yield
`(%)
`
`66.1
`73.9
`79.7
`81.2
`79.2
`83.5
`
`SD
`
`1.9
`3.5
`5.5
`11.6
`7.3
`16.5
`
`Yield
`(%)
`
`63.3
`73.7
`81.2
`83.4
`77.9
`74.1
`
`SD
`
`2.9
`4.6
`6.1
`2.3
`5.9
`3.1
`
`Yield
`(%)
`
`58.9
`68.1
`83.3
`84.0
`84.7
`79.5
`
`SD
`
`6.0
`4.8
`4.3
`2.4
`3.8
`4.0
`
`Yield
`(%)
`
`32.9
`53.2
`67.5
`74.9
`82.6
`84.3
`
`SD
`
`2.9
`0.4
`7.6
`6.6
`3.9
`8.3
`
`Yield
`(%)
`
`—
`21.5
`33.2
`43.5
`51.7
`56.4
`
`SD
`
`—
`0.4
`3.4
`1.1
`3.5
`0.9
`
`Yield
`(%)
`
`—
`—
`—
`17.3
`21.3
`23.3
`
`SD
`
`—
`—
`—
`1.6
`1.2
`3.5
`
`572
`
`BIOTECHNOLOGY AND BIOENGINEERING, VOL. 83, NO. 5, SEPTEMBER 5, 2003
`
`Page 6
`
`

`

`The experiments conducted at higher lysozyme concen-
`tration showed a decreasing refolding yield as the concen-
`tration of lysozyme increased, for all chemical composi-
`tions, although the decrease in yield was more pronounced
`at low concentrations of urea and DTT (Table VI). The
`aggregation rate constants were obtained by regression to a
`first- and third-order reaction scheme, with the refolding
`rate fixed to values in Table II. Figure 4 shows the regres-
`sion fit of the first- and third-order reaction scheme for one
`of the chemical compositions. Unlike the refolding rate con-
`stant, the general trend was for the aggregation rate constant
`to decrease from 8.10 mL2 mg−2 min−1 to 3.79 mL2 mg−2
`min−1 as the urea and DTT concentrations increased. This
`decrease in the aggregation rate constant is probably due to
`the increase in urea concentration. In these experiments the
`concentrations of DTT and urea were both varied together
`to give snapshots of the chemical environments experienced
`during fed-batch refolding (see Introduction). It is not nec-
`essary to conclusively decouple the effects of DTT and urea
`variation.
`To fully model a fed-batch refolding process it is neces-
`sary to have a continuous function relating the refolding and
`aggregation rate constants to the changing chemical com-
`position. Expressions do exist that relate the refolding and
`aggregation rate constants to denaturant concentration (Cle-
`land and Wang, 1990; Hevehan and De Bernardez Clark,
`1997; Vicik and De Bernardez Clark, 1991). However these
`expressions are not useful in this case since the redox po-
`tential of the refold buffer also changed during the fed-batch
`
`Figure 4. Selected yield data from Table III for a chemical composition
`of 0.36M urea and 1.44 mM DTT showing the modeled yield based on the
`competing first- and third-order scheme shown in Figure 2, with least sum
`of squares regression to the data to give the rate constants shown in Table
`VI. Error bars represent 1 standard deviation for triplicate experiments. The
`maximum yield was set to 80%.
`
`Figure 3. Selected yield data from Table II, for a chemical composition
`of 0.36M urea and 1.44 mM DTT and total lysozyme concentrations of
`0.025 mg/mL−1 (closed symbols) and 0.05 mg/mL−1 (open symbols),
`showing the first-order rate law regression (solid line). Error bars represent
`1 standard deviation for triplicate experiments. The maximum yield was set
`to 80%.
`
`some material is not active after refolding, presumably due
`to incorrect disulphide bond formation (Roux et al., 1997;
`Saxena and Wetlaufer, 1970;). This effect has also been
`observed for insulin-like growth factors (Milner et al.,
`1995).
`The refolding rate constants obtained by regression of the
`data to a first-order rate law are shown in Table II for the
`various “snapshot” conditions representative of our selected
`fed-batch protocol. At the lowest urea and DTT concentra-
`tions, the refolding rate constant was 0.022 min−1 increasing
`to 0.175 min−1 at the highest concentrations investigated.
`These conditions correspond to the initial and final chemical
`compositions of the fed-batch refolding experiment, respec-
`tively. The increasing concentration of urea might be ex-
`pected to destabilize native structure and the refolding rate
`constant should therefore decrease with increasing urea con-
`centration. However, the final urea concentration was well
`below the denaturation midpoint for lysozyme and at these
`concentrations is unlikely to have a significant effect on the
`refolding rate constant (Greene and Pace, 1974). The in-
`crease in the refolding rate constant is most likely related to
`the increase in DTT concentration. The presence of a re-
`ducing agent is necessary during the oxidative renaturation
`of proteins containing disulphide bonds as it facilitates di-
`sulphide shuffling (Fischer et al., 1992). Presumably, if the
`concentrations of urea and DTT were increased further a
`point would occur where the refolding rate constant would
`begin to decrease as the concentration of urea approached
`the denaturation midpoint for the protein, and the chemical
`environment became excessively reducing.
`
`BUSWELL AND MIDDELBERG: A NEW KINETIC SCHEME FOR LYSOZYME REFOLDING AND AGGREGATION
`
`573
`
`Page 7
`
`

`

`A New Kinetic Scheme for Lysozyme:
`Independent Paramaterization
`
`The effective yield from batch experiments where native
`lysozyme was present in the refolding buffer prior to dilu-
`tion is shown in Table IV. The presence of native lysozyme
`at concentrations likely to occur during fed-batch refolding
`significantly decreased the e