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Pseudo First-Order Cleavage of an Immobilized Substrate by an Enzyme Undergoing Two-Dimensional Surface Diffusion
Journal of Colloid and Interface Science 213, 81– 86 (1999) Article ID jcis.1999.6109, available online at http://www.idealibrary.com on
Pseudo First-Order Cleavage of an Immobilized Substrate by an Enzyme Undergoing Two-Dimensional Surface Diffusion Giuseppe Trigiante,* Alice P. Gast,† ,1 and Channing R. Robertson† ,1 *Department of Chemistry, and †Department of Chemical Engineering, Stanford University, Stanford, California 94305-5025 Received June 19, 1998; accepted January 28, 1999
at a given spatial location, collagenase is both irreversibly adsorbed and able to translate by diffusion on the substrate surface (3). We studied the kinetic behavior of this twodimensional reaction/diffusion system as a means of characterizing the relationship between diffusion and chemical reactivity of the surface-associated yet mobile enzyme species. Our reaction system consisted of a flow cell (Fig. 1) that allowed us to monitor the cumulative absorbance of ten slide surfaces, while being continuously flushed with a buffer to remove the cleaved portion of the substrate. As a result, we could assess the extent of reaction by measuring the reduction in absorbance accompanying substrate cleavage. This experimental system was discussed in an earlier publication (1). In the previous treatment, the reaction/diffusion system was described by means of the Smoluchowski theory, a mathematical solution for a classical two-dimensional “heatsink” problem, whose premises were similar to our experimental situation. In this report we present new experimental data and propose an alternative and improved theoretical analysis, proceeding from a completely different model of the reaction, that allows us to more accurately represent the experimental data and also propose certain hypotheses about the governing reaction mechanism.
In this paper we study the reaction kinetics of an enzyme adsorbed on a peptide substrate surface. Although the adsorption is effectively irreversible, the enzyme is able to diffuse on the surface. Our reaction system consisted of the enzyme collagenase and the oligopeptide FALGPA, a substrate for the enzyme. A quartz surface was coated with covalently bound substrate molecules. The extent of reaction was monitored continuously in a flow cell via UV absorption. The data are compatible with a kinetic model based on a pseudo first-order diffusion/orientation ratelimiting step followed by a relatively fast chemical cleavage step. This model was validated by examining the pH dependence of the rate constant. © 1999 Academic Press Key Words: enzymes; collagenase; FALGPA; surface diffusion; enzyme kinetics.
INTRODUCTION
Enzymatic reactions at surfaces are of interest both for their occurrence in nature (membrane-bound enzyme reactions at the surface of cells) and for the insights they provide on the stereochemistry of chemical processes. The interactions between proteins and surfaces, either biological or synthetic, have potential applications in areas such as medical implants, affinity separations, assays, and sensors (1). Binding both enzymes and their substrates to surfaces leads to interesting and unexpected relations between chemical interactions and physical/ diffusion phenomena. The enzyme considered in this paper and in our previous work (1) is Clostridium Histolyticum collagenase, a 100-kDa enzyme that cleaves collagen at a known amino acid sequence. The oligopeptide furanacryloyl–alanine–leucine– glycine–proline–alanine (FALGPA) provides this sequence and is a preferred substrate because of its solubility in water and its characteristic spectrophotometric behavior during the reaction. The enzyme cleaves the peptide at the ala–leu peptide bond and the resulting furanacryloyl absorbance peak is shifted to lower wavelengths (2). In our system, FALGPA is covalently attached to the surface of quartz slides and collagenase is subsequently adsorbed (1). While FALGPA is permanently fixed 1
MATERIALS AND METHODS
Collagenase from Clostridium Histolyticum (type VII), FALGPA, and EDAC (1-ethyl-3-(3-dimethylaminopropyl) carbodiimide) were purchased from Sigma and used without further purification. Quartz microscope slides, 3 3 1 in. (code CGQ-0640-01) were obtained from Chemglass. Aminopropyltriethoxysilane (ATES) was obtained from Sigma. Spectroscopy measurements were performed with a HP 8452A diode array spectrometer. All the chemicals used for the buffers were also obtained from Sigma, except EDTA (Gibco) and CaCl 2 (Mallinkrodt). Buffer Solutions All of the reactions were carried out in specifically formulated buffer solutions. Their main purpose, aside from providing a pH-controlled reaction environment, was also to control the enzyme reactivity. Since it is known that collagenase
To whom correspondence should be addressed. 81
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creased to 4.0 following completion of the reaction. The slides were left to react for 12 h at room temperature. Subsequently the solution was removed and the slides rinsed with DI water, dried at room temperature, and stored. Quantitation of Enzyme Adsorption on Derivatized Slides
FIG. 1. The FALGPA/collagenase reaction cell.
requires calcium ions for its activation, two buffers were designated as “inactive” and “active.” The first contained the calcium chelating agent EDTA to ensure calcium concentrations low enough to inhibit the reaction. The second provided the ion, thus promoting reactivity.
A 100 mg/mL solution of collagenase in inactive buffer was prepared. Three aliquots (40 mL each) were placed on three slides derivatized as described above. Each was then covered with another derivatized glass slide with interposed 0.18-mm spacers so that the liquid would contact a surface 4.4 cm 2 in area. After variable contact times (15, 30, 60 min) each liquid aliquot was retrieved and added to 960 mL of a 0.1 mM solution of FALGPA in active buffer. Absorbance at 324 nm was subsequently monitored at room temperature and the time constant of the first-order cleavage reaction (t) was determined from semilogarithmic kinetic rate plots and reported in Table 1. The bulk enzyme concentration ([E]) is related to t by
t5
Inactive buffer: 50 mM Tricine, 0.43 M NaCl, 10 mM EDTA, pH 7.5 Active buffer: 50 mM Tricine, 0.43 M NaCl, 10 mM CaCl 2, pH 7.5 For the pH-dependence studies, a low-pH active buffer was employed containing MES (2(N-morpholino) ethanesulfonic acid) 50 mM, pH 6.05, instead of Tricine.
D
21
,
[1]
where k cat is the chemical step rate constant which is reported to be 18.3 s 21 in solution and K m , the Michaelis–Menten constant, is reported to be 0.5 mM (2). Given that t and [E] are inversely proportional, the latter was determined by the relation @E# t0 5 , @E# 0 t
Slide Preparation and Derivatization The quartz slides, whether new or used, were prepared as described previously (1). Briefly, they were soaked in NaOH heated at 80°C, then rinsed with cold 0.1 M HCl, and air dried. This ensured complete removal of cross-linked reaction products. For silanization, the slides were placed in warm (37°C) acetone for 1 h, after which ATES (0.1% v/v) was added to the acetone solution. After 1 h the silanization reaction was stopped by removing the slides and rinsing them with deionized (DI) water. The slides were dried at room temperature and successful silanization was ascertained by contact angle measurement and surface XPS. Cleaned slides were used as a reference for both experiments. The contact angle increased following silanization from an average of 30° to about 50 –55°. XPS confirmed silanization by detecting nitrogen atoms on the slide surface, whereas none was detectable on the reference slides. To initiate FALGPA peptide cross-linking to the silanized slides, a 1 mM FALGPA solution was prepared in water. As soon as the FALGPA was dissolved, 2.5 mM EDAC was added and the solution was placed in contact with the six slides (1 mL/side of slide) needed for the experiment. This was accomplished by inserting the slides into the reaction cell (Fig. 1) whose chambers were later filled with the cross-linking solution and sealed. The solution pH was initially 4.3 and de-
S
k cat @E# Km
[2]
where t 0 and [E] 0 refer to the unexposed solution. The difference in enzyme concentration between the original solution and the one exposed to the slides was attributed to enzyme adsorption on the slide surfaces and thus the specific adsorption per unit area was determined (Table 1). Protocol for the 2D Experiment The experiment was conducted in the reaction cell depicted in Fig. 1. The six slides were assembled and the compartments filled with collagenase solution (100 mg/mL inactive buffer,
TABLE 1 Results of the Collagenase/Quartz Adsorption Assay Contact time (min)
t a (s)
[E] (mg/mL)
[E] sur (mg/cm 2)
0 15 30 60
1100 1850 1930 1980
100.00 59.46 56.99 55.56
0.00 0.36 0.39 0.40
t is the reciprocal of the slope of the linear fit to the semilogarithmic plot of the reaction kinetics (shown in Fig. 2). a
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ENZYME KINETICS AT SURFACES
FIG. 2. Semilogarithmic plot of the collagenase adsorption spectrophotometric assay reactions (A, unexposed solution; B, C, D, 15, 30, and 60 min exposure, respectively). The ordinate reports 2ln( A 2 A end)/( A 0 2 A end) where A, A 0 , and A end are, respectively, the absorption at time t, time zero, and 3 h. The fit lines (whose corresponding time constants t are listed in Table 1) are omitted for clarity.
pH 7.5). After 1 h at room temperature the collagenase solution was removed and the compartments flushed with inactive buffer for about 2 h, at a flow rate of 1 mL/min, by means of a peristaltic pump. During this time, absorbance (304 nm) was monitored every 30 s after positioning the cell in the optical path of the spectrometer in order to ascertain the presence of a stable baseline measurement. The cell was oriented at an angle of about 35° with respect to the optical axis to improve the signal-to-noise ratio by minimizing stray reflections and increasing the amount of substrate in the optical path. When the absorbance reached a constant value, the cell was emptied of inactive buffer and refilled with recirculating active buffer at a flow rate of 1 mL/min. The inactive buffer was completely removed before introducing the active buffer to avoid mixing of EDTA and calcium. The flow rate was chosen to give a space time of 2 min to guarantee prompt removal of the hydrolyzed product while still being low enough to avoid excessive shear at the surface (shear rate: 1.4 s 21). As soon as the compartments were filled with flowing active buffer, the absorbance was recorded every 30 s for 24 h. Two absorbance wavelengths were monitored, 304 and 278 nm, the former (denoted A) corresponding to the typical FALGPA absorption peak and the latter an indicator of protein concentration and/or instrumental drifts, and therefore ideally a value that should remain constant. The absorbance at 304 nm at the end of the experiment (12–14 h after the absorbance stabilized, denoted A end) was used as the reaction endpoint value, and the difference between the starting and ending points ( A 0 2 A end) was used to determine the hydrolyzable substrate concentration on the slides.
shown in Fig. 2 in semilog format. The ordinate reports the value of 2ln[( A 2 A end)/( A 0 2 A end)], where A, A 0 , and A end are, respectively, the absorbance at time t, time zero, and following completion (3-h reaction time for these measurements). As it absorbs onto the surface, the enzyme is removed from the solution. By knowing the bulk enzyme concentration at the beginning (t 5 0) it is possible, through the rate of the first-order hydrolysis reaction, to obtain the residual bulk enzyme concentration and thus the adsorbed surface enzyme concentration (Table 1). The surface is saturated within 15 min and prolonged exposure does not significantly increase the enzyme surface concentration. The asymptotic surface concentration is [E] sur,max 5 0.4 mg/cm 2 for a bulk concentration of 100 mg/mL. 2D Reaction Results A typical reaction experiment at pH 7.5 is shown in Fig. 3a. The ordinate [F]/[F] 0 is defined as the concentration ratio of uncleaved surface-bound FALGPA at any given time ([F]) to the one at t 5 0 ([F] 0 ), and obtained by the formula @F# ~ A 2 A end! 5 , @F# 0 ~ A 0 2 A end!
[3]
where A 0 is the initial and A end the end-value absorbance readings, taken as described above. A fit for each curve is superimposed according to the kinetic model and the assump-
RESULTS
Enzyme Adsorption on Derivatized Slides The assay used to measure surface enzyme concentrations proved to be precise and reproducible. One of the series is
FIG. 3. Kinetics of the hydrolysis of FALGPA by collagenase as monitored by spectrophotometry. The parameter [F]/[F] 0 measures the fraction of unreacted substrate. First-order fits are overlaid (dashed lines) and the corresponding rate constants are defined as k. (a) pH 7.5, k 5 3.3 3 10 25 s 21; (b) pH 6.05, k 5 11 3 10 25 s 21.
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lead to reaction because of the statistically low probability of the species meeting with a proper spatial orientation. A small number of encounters, though, may lead to the formation of a reactive complex (EF*) which chemically reacts to release the enzyme plus the cleaved product. E1F
kO
kc
¡ EF* ¡ E 1 P SCHEME 1
FIG. 4. Previously reported (1) results of the FALGPA/collagenase reaction at pH 7.5 together with a first-order fit curve (time constant: 11 h).
tions made in the Discussion section. For most of the time course, the fit curves and the data are indistinguishable. The hydrolyzable FALGPA surface concentration, determined from the starting and ending points of each reaction, was on the order of 10 14 molecules/cm 2, although individual values could vary. This is consistent with previously reported values (1). One experiment at a lower pH (6.05) is also displayed (Fig. 3b), together with the model curve representing the best fit to the data. DISCUSSION
The surface-bound collagenase and FALGPA reaction has been studied previously and a model suggested for the interpretation of the kinetics (1). The model involved a mathematical formulation based on the Smoluchowski treatment for heat conduction from a cylinder whose boundaries are maintained isothermal. This model offers interesting applications in chemistry as its conditions are often recurrent in kinetic systems; however, under the experimental conditions herein, the solution to the Smoluchowski model equation is not well behaved, thereby rendering comparison of experiment and theory problematic. The alternative model we present in this paper overcomes these difficulties. The adsorbed enzyme molecules are retained on the quartz slide by multiple noncovalent interactions, which nevertheless sum up to give a binding energy high enough to ensure essentially irreversible adsorption, as previously shown (3). In the same paper it was also shown that the majority of enzyme molecules are mobile on the surface with a two-dimensional diffusion coefficient of D 5 9 3 10 210 cm 2/s. Therefore one can model the reaction system as a plane with substrate molecules covalently anchored to it and enzyme molecules sliding (or rolling) across it. Each time an enzyme (E) molecule encounters a substrate (F), an adduct (EF) is formed. This adduct does not generally
The rate constant for the chemical step on the surface is denoted k c to distinguish it from the corresponding parameter in solution (k cat). Overall, we have the two-step kinetic model outlined in Scheme 1. We implicitly assume that we can combine diffusion and orientation into a single step leading to the formation of a reactive complex. These rate processes can be described by the following set of equations: d@EF*# 5 k o@E#@F# 2 k c @EF*# dt
[4]
d@F# 5 2k o@E#@F# dt
[5]
d@P# 5 k c @EF*# dt
[6]
@F# 1 @EF*# 1 @P# 5 F 0
(substrate balance)
[7]
In general they lead to a complex kinetic solution. Simplification results by assuming that the rate of formation of the active complex is very different from the rate of the chemical cleavage step, so that the free enzyme concentration [E], and hence the active complex concentration [EF*], are approximately constant. Given this assumption, Eqs. [4] to [7] reduce to d@P# 5 k o@E#~F o 2 @P#! dt d@P# 5 k c ~F o 2 @P#! dt
k c @ k o@E#
k o@E# @ k c .
[8]
[9]
Integrating Eqs. [8] and [9] gives P 5 F o~1 2 e 2k o@E#t ! P 5 F o~1 2 e 2k ct !
k c @ k o@E# k o@E# @ k c .
[10] [11]
Equations [10] and [11] correspond to a pseudo first and a first-order reaction rate, respectively. To verify these relations we fit the experimental data with a first-order exponential, as shown in Figs. 3a, 3b, and 4, the
85
ENZYME KINETICS AT SURFACES
latter being previously published experimental results (1). The semilog plots for Figs. 3a and 3b are shown in Fig. 5. The reactions follow first (or pseudo first)-order kinetics. These results confirm the assumption that one of the two steps is much slower than the other while still not discriminating between the two cases. The rate-limiting step must either be the chemical one (hydrolysis of the EF* complex) or the diffusion/orientational step (formation of the EF* complex). To discriminate between these possibilities, we conducted a series of experiments at a lower pH. Collagenase activity in the bulk (as expressed by k cat) is maximal at pH 7.5 and decreases about 3-fold at pH 6 (2). The data from our experiments (Fig. 3), however, together with the model overlay (Fig. 5), show an increase (3- to 4-fold) rather than a decrease in reaction rate at pH 6.05. This suggests that enzymatic cleavage is not the rate-limiting step and that the formation rate of the enzyme complex is enhanced at lower pHs. While it is possible that the dependence of enzyme activity on pH may be different on a surface than it is in solution, the decrease in the observed overall rate with respect to the bulk or solution k cat (about 5 3 10 5-fold) strongly suggests that the slow step is qualitatively different in this case. Results from two previous studies support this conclusion. First, Sandwick and Schray (4) demonstrated that enzymes adsorbed to surfaces at high concentrations retain a significant fraction of their solution activity. In our experiments, the enzyme is adsorbed at saturating levels and surface concentration is as high as it can become. Second, with respect to the effect of pH on enzyme activity, Russell and Fersht (5) showed that at low ionic strengths (,100 mM) there was indeed a measurable dependence. At higher ionic strengths such as the ones used in this study (.500 mM), however, this dependence all but disappeared. This is thought to be due to electrostatic screening of the active site. Previously reported results using surface-bound substrates (1) also show increases in the overall reaction rate at low pH (Fig. 6). The influence of pH on enzymatic activity at surfaces is complex due to the changing structure of the protein and the substrate due to the
FIG. 5. Semilogarithmic plots of the FALGPA hydrolysis reactions shown in Fig. 3.
FIG. 6. Previously reported (1) results of FALGPA/collagenase reactions at low pH. First-order fit curves are overlaid (dashed lines).
titration of ionizable groups. The isoelectric point (pI) of collagenase A is 8.6 (6) and it contains 16 histidines, each having a pI of 6.0. The charge of the quartz surface is unlikely to change at pH 6 as the surface silicates have a pI lower than 4. The cleavage product of FALGPA has a terminal amino group whose pK is greater than 8, and thus it is protonated at both pH 6 and pH 7. It is likely that the observed changes occur because of a decrease in energy of the weak bonds that restrict the overall enzyme mobility (both translational and orientational) due to titration of charged moieties on the enzyme molecule. The kinetic data allow some inference about the nature of the enzyme-surface bonds. The overall rate constant k at pH 7.5 measured from the plots (Figs. 3a and 5) corresponds to k o[E] in our model and is equal to 3.3 3 10 25 s 21. This implies an initial enzyme turnover rate of d@F# U @E#dt U
5
k o@E#@F O# @E#
5
~3.3 3 10 25 ! 3 ~2 3 10 210 ! 5 0.002 s 21. 4 3 10 212
t50
The corresponding value of the initial enzyme turnover rate at pH 6.05 is larger but on the same order of magnitude. By assuming that the mean free path of an enzyme molecule is the average distance between substrates, around 14 Å (1), and by knowing the 2D diffusion coefficient (3), we can estimate a frequency of EF encounters of 10 5/s per molecule. It is apparent that the majority of encounters have a consistently unfavorable orientation to react, and this suggests that the enzyme is restrained in its orientation as it moves along the surface (7). Put in another way, the conformation that minimizes the adsorption free energy is not favorable for substrate binding; hence, most of the complexes formed are unreactive. It would be interesting to have the 3D structure of collage-
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TRIGIANTE, GAST, AND ROBERTSON
nase available so as to propose hypotheses about the nature of the enzyme/peptide contact orientation, but unfortunately it is not known at this time (8).
ing. The reaction is therefore diffusion and/or orientation controlled and from the value of the rate constant the conclusion can be drawn that the enzyme/derivatized surface bond may involve a preferred, nonrandom orientation of the enzyme.
SUMMARY
The reaction between adsorbed Clostridium collagenase and the covalently surface bound model substrate FALGPA displays pseudo first-order kinetic behavior. A two-step model is developed to describe the reaction, consisting of a diffusioncontrolled process in which the reactants form a complex capable of chemically reacting, followed by a chemical cleavage step. The first- or pseudo first-order nature of the observed kinetics suggests that one of the two steps is rate-limiting. The substantial decline in the reaction rate, together with a pH dependence that is reversed with respect to that in solution, indicate that the chemical cleavage step is not rate-determin-
REFERENCES 1. Gaspers, P., Gast, A. P., and Robertson, C. R., J. Colloid Interface Sci. 172, 518 (1995). 2. van Wart, H. E., and Steinbrink, R., Anal. Biochem. 113, 356 (1981). 3. Gaspers, P., Gast, A. P., and Robertson, C. R., Langmuir 10, 2699 (1994). 4. Sandwick, R. K., and Schray, K. J., J. Colloid Interface Sci. 121, 1 (1988). 5. Russell, A. J., and Fersht, A. R., Nature 328, No. 6, 496 (1987). 6. Nordwig, A., Leder 13, 10 (1962). 7. Robeson, J. L., and Tilton, R. D., Langmuir 12, 6104 (1996). 8. Matsushita, O., Chang-Min, J., Minami, J., Katayama, S., Nishi, N., and Okabe, A., J. Biol. Chem. 273, No. 6, 3643 (1998).
Pseudo First-Order Cleavage of an Immobilized Substrate by an Enzyme Undergoing Two-Dimensional Surface Diffusion Giuseppe Trigiante,* Alice P. Gast,† ,1 and Channing R. Robertson† ,1 *Department of Chemistry, and †Department of Chemical Engineering, Stanford University, Stanford, California 94305-5025 Received June 19, 1998; accepted January 28, 1999
at a given spatial location, collagenase is both irreversibly adsorbed and able to translate by diffusion on the substrate surface (3). We studied the kinetic behavior of this twodimensional reaction/diffusion system as a means of characterizing the relationship between diffusion and chemical reactivity of the surface-associated yet mobile enzyme species. Our reaction system consisted of a flow cell (Fig. 1) that allowed us to monitor the cumulative absorbance of ten slide surfaces, while being continuously flushed with a buffer to remove the cleaved portion of the substrate. As a result, we could assess the extent of reaction by measuring the reduction in absorbance accompanying substrate cleavage. This experimental system was discussed in an earlier publication (1). In the previous treatment, the reaction/diffusion system was described by means of the Smoluchowski theory, a mathematical solution for a classical two-dimensional “heatsink” problem, whose premises were similar to our experimental situation. In this report we present new experimental data and propose an alternative and improved theoretical analysis, proceeding from a completely different model of the reaction, that allows us to more accurately represent the experimental data and also propose certain hypotheses about the governing reaction mechanism.
In this paper we study the reaction kinetics of an enzyme adsorbed on a peptide substrate surface. Although the adsorption is effectively irreversible, the enzyme is able to diffuse on the surface. Our reaction system consisted of the enzyme collagenase and the oligopeptide FALGPA, a substrate for the enzyme. A quartz surface was coated with covalently bound substrate molecules. The extent of reaction was monitored continuously in a flow cell via UV absorption. The data are compatible with a kinetic model based on a pseudo first-order diffusion/orientation ratelimiting step followed by a relatively fast chemical cleavage step. This model was validated by examining the pH dependence of the rate constant. © 1999 Academic Press Key Words: enzymes; collagenase; FALGPA; surface diffusion; enzyme kinetics.
INTRODUCTION
Enzymatic reactions at surfaces are of interest both for their occurrence in nature (membrane-bound enzyme reactions at the surface of cells) and for the insights they provide on the stereochemistry of chemical processes. The interactions between proteins and surfaces, either biological or synthetic, have potential applications in areas such as medical implants, affinity separations, assays, and sensors (1). Binding both enzymes and their substrates to surfaces leads to interesting and unexpected relations between chemical interactions and physical/ diffusion phenomena. The enzyme considered in this paper and in our previous work (1) is Clostridium Histolyticum collagenase, a 100-kDa enzyme that cleaves collagen at a known amino acid sequence. The oligopeptide furanacryloyl–alanine–leucine– glycine–proline–alanine (FALGPA) provides this sequence and is a preferred substrate because of its solubility in water and its characteristic spectrophotometric behavior during the reaction. The enzyme cleaves the peptide at the ala–leu peptide bond and the resulting furanacryloyl absorbance peak is shifted to lower wavelengths (2). In our system, FALGPA is covalently attached to the surface of quartz slides and collagenase is subsequently adsorbed (1). While FALGPA is permanently fixed 1
MATERIALS AND METHODS
Collagenase from Clostridium Histolyticum (type VII), FALGPA, and EDAC (1-ethyl-3-(3-dimethylaminopropyl) carbodiimide) were purchased from Sigma and used without further purification. Quartz microscope slides, 3 3 1 in. (code CGQ-0640-01) were obtained from Chemglass. Aminopropyltriethoxysilane (ATES) was obtained from Sigma. Spectroscopy measurements were performed with a HP 8452A diode array spectrometer. All the chemicals used for the buffers were also obtained from Sigma, except EDTA (Gibco) and CaCl 2 (Mallinkrodt). Buffer Solutions All of the reactions were carried out in specifically formulated buffer solutions. Their main purpose, aside from providing a pH-controlled reaction environment, was also to control the enzyme reactivity. Since it is known that collagenase
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TRIGIANTE, GAST, AND ROBERTSON
creased to 4.0 following completion of the reaction. The slides were left to react for 12 h at room temperature. Subsequently the solution was removed and the slides rinsed with DI water, dried at room temperature, and stored. Quantitation of Enzyme Adsorption on Derivatized Slides
FIG. 1. The FALGPA/collagenase reaction cell.
requires calcium ions for its activation, two buffers were designated as “inactive” and “active.” The first contained the calcium chelating agent EDTA to ensure calcium concentrations low enough to inhibit the reaction. The second provided the ion, thus promoting reactivity.
A 100 mg/mL solution of collagenase in inactive buffer was prepared. Three aliquots (40 mL each) were placed on three slides derivatized as described above. Each was then covered with another derivatized glass slide with interposed 0.18-mm spacers so that the liquid would contact a surface 4.4 cm 2 in area. After variable contact times (15, 30, 60 min) each liquid aliquot was retrieved and added to 960 mL of a 0.1 mM solution of FALGPA in active buffer. Absorbance at 324 nm was subsequently monitored at room temperature and the time constant of the first-order cleavage reaction (t) was determined from semilogarithmic kinetic rate plots and reported in Table 1. The bulk enzyme concentration ([E]) is related to t by
t5
Inactive buffer: 50 mM Tricine, 0.43 M NaCl, 10 mM EDTA, pH 7.5 Active buffer: 50 mM Tricine, 0.43 M NaCl, 10 mM CaCl 2, pH 7.5 For the pH-dependence studies, a low-pH active buffer was employed containing MES (2(N-morpholino) ethanesulfonic acid) 50 mM, pH 6.05, instead of Tricine.
D
21
,
[1]
where k cat is the chemical step rate constant which is reported to be 18.3 s 21 in solution and K m , the Michaelis–Menten constant, is reported to be 0.5 mM (2). Given that t and [E] are inversely proportional, the latter was determined by the relation @E# t0 5 , @E# 0 t
Slide Preparation and Derivatization The quartz slides, whether new or used, were prepared as described previously (1). Briefly, they were soaked in NaOH heated at 80°C, then rinsed with cold 0.1 M HCl, and air dried. This ensured complete removal of cross-linked reaction products. For silanization, the slides were placed in warm (37°C) acetone for 1 h, after which ATES (0.1% v/v) was added to the acetone solution. After 1 h the silanization reaction was stopped by removing the slides and rinsing them with deionized (DI) water. The slides were dried at room temperature and successful silanization was ascertained by contact angle measurement and surface XPS. Cleaned slides were used as a reference for both experiments. The contact angle increased following silanization from an average of 30° to about 50 –55°. XPS confirmed silanization by detecting nitrogen atoms on the slide surface, whereas none was detectable on the reference slides. To initiate FALGPA peptide cross-linking to the silanized slides, a 1 mM FALGPA solution was prepared in water. As soon as the FALGPA was dissolved, 2.5 mM EDAC was added and the solution was placed in contact with the six slides (1 mL/side of slide) needed for the experiment. This was accomplished by inserting the slides into the reaction cell (Fig. 1) whose chambers were later filled with the cross-linking solution and sealed. The solution pH was initially 4.3 and de-
S
k cat @E# Km
[2]
where t 0 and [E] 0 refer to the unexposed solution. The difference in enzyme concentration between the original solution and the one exposed to the slides was attributed to enzyme adsorption on the slide surfaces and thus the specific adsorption per unit area was determined (Table 1). Protocol for the 2D Experiment The experiment was conducted in the reaction cell depicted in Fig. 1. The six slides were assembled and the compartments filled with collagenase solution (100 mg/mL inactive buffer,
TABLE 1 Results of the Collagenase/Quartz Adsorption Assay Contact time (min)
t a (s)
[E] (mg/mL)
[E] sur (mg/cm 2)
0 15 30 60
1100 1850 1930 1980
100.00 59.46 56.99 55.56
0.00 0.36 0.39 0.40
t is the reciprocal of the slope of the linear fit to the semilogarithmic plot of the reaction kinetics (shown in Fig. 2). a
83
ENZYME KINETICS AT SURFACES
FIG. 2. Semilogarithmic plot of the collagenase adsorption spectrophotometric assay reactions (A, unexposed solution; B, C, D, 15, 30, and 60 min exposure, respectively). The ordinate reports 2ln( A 2 A end)/( A 0 2 A end) where A, A 0 , and A end are, respectively, the absorption at time t, time zero, and 3 h. The fit lines (whose corresponding time constants t are listed in Table 1) are omitted for clarity.
pH 7.5). After 1 h at room temperature the collagenase solution was removed and the compartments flushed with inactive buffer for about 2 h, at a flow rate of 1 mL/min, by means of a peristaltic pump. During this time, absorbance (304 nm) was monitored every 30 s after positioning the cell in the optical path of the spectrometer in order to ascertain the presence of a stable baseline measurement. The cell was oriented at an angle of about 35° with respect to the optical axis to improve the signal-to-noise ratio by minimizing stray reflections and increasing the amount of substrate in the optical path. When the absorbance reached a constant value, the cell was emptied of inactive buffer and refilled with recirculating active buffer at a flow rate of 1 mL/min. The inactive buffer was completely removed before introducing the active buffer to avoid mixing of EDTA and calcium. The flow rate was chosen to give a space time of 2 min to guarantee prompt removal of the hydrolyzed product while still being low enough to avoid excessive shear at the surface (shear rate: 1.4 s 21). As soon as the compartments were filled with flowing active buffer, the absorbance was recorded every 30 s for 24 h. Two absorbance wavelengths were monitored, 304 and 278 nm, the former (denoted A) corresponding to the typical FALGPA absorption peak and the latter an indicator of protein concentration and/or instrumental drifts, and therefore ideally a value that should remain constant. The absorbance at 304 nm at the end of the experiment (12–14 h after the absorbance stabilized, denoted A end) was used as the reaction endpoint value, and the difference between the starting and ending points ( A 0 2 A end) was used to determine the hydrolyzable substrate concentration on the slides.
shown in Fig. 2 in semilog format. The ordinate reports the value of 2ln[( A 2 A end)/( A 0 2 A end)], where A, A 0 , and A end are, respectively, the absorbance at time t, time zero, and following completion (3-h reaction time for these measurements). As it absorbs onto the surface, the enzyme is removed from the solution. By knowing the bulk enzyme concentration at the beginning (t 5 0) it is possible, through the rate of the first-order hydrolysis reaction, to obtain the residual bulk enzyme concentration and thus the adsorbed surface enzyme concentration (Table 1). The surface is saturated within 15 min and prolonged exposure does not significantly increase the enzyme surface concentration. The asymptotic surface concentration is [E] sur,max 5 0.4 mg/cm 2 for a bulk concentration of 100 mg/mL. 2D Reaction Results A typical reaction experiment at pH 7.5 is shown in Fig. 3a. The ordinate [F]/[F] 0 is defined as the concentration ratio of uncleaved surface-bound FALGPA at any given time ([F]) to the one at t 5 0 ([F] 0 ), and obtained by the formula @F# ~ A 2 A end! 5 , @F# 0 ~ A 0 2 A end!
[3]
where A 0 is the initial and A end the end-value absorbance readings, taken as described above. A fit for each curve is superimposed according to the kinetic model and the assump-
RESULTS
Enzyme Adsorption on Derivatized Slides The assay used to measure surface enzyme concentrations proved to be precise and reproducible. One of the series is
FIG. 3. Kinetics of the hydrolysis of FALGPA by collagenase as monitored by spectrophotometry. The parameter [F]/[F] 0 measures the fraction of unreacted substrate. First-order fits are overlaid (dashed lines) and the corresponding rate constants are defined as k. (a) pH 7.5, k 5 3.3 3 10 25 s 21; (b) pH 6.05, k 5 11 3 10 25 s 21.
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lead to reaction because of the statistically low probability of the species meeting with a proper spatial orientation. A small number of encounters, though, may lead to the formation of a reactive complex (EF*) which chemically reacts to release the enzyme plus the cleaved product. E1F
kO
kc
¡ EF* ¡ E 1 P SCHEME 1
FIG. 4. Previously reported (1) results of the FALGPA/collagenase reaction at pH 7.5 together with a first-order fit curve (time constant: 11 h).
tions made in the Discussion section. For most of the time course, the fit curves and the data are indistinguishable. The hydrolyzable FALGPA surface concentration, determined from the starting and ending points of each reaction, was on the order of 10 14 molecules/cm 2, although individual values could vary. This is consistent with previously reported values (1). One experiment at a lower pH (6.05) is also displayed (Fig. 3b), together with the model curve representing the best fit to the data. DISCUSSION
The surface-bound collagenase and FALGPA reaction has been studied previously and a model suggested for the interpretation of the kinetics (1). The model involved a mathematical formulation based on the Smoluchowski treatment for heat conduction from a cylinder whose boundaries are maintained isothermal. This model offers interesting applications in chemistry as its conditions are often recurrent in kinetic systems; however, under the experimental conditions herein, the solution to the Smoluchowski model equation is not well behaved, thereby rendering comparison of experiment and theory problematic. The alternative model we present in this paper overcomes these difficulties. The adsorbed enzyme molecules are retained on the quartz slide by multiple noncovalent interactions, which nevertheless sum up to give a binding energy high enough to ensure essentially irreversible adsorption, as previously shown (3). In the same paper it was also shown that the majority of enzyme molecules are mobile on the surface with a two-dimensional diffusion coefficient of D 5 9 3 10 210 cm 2/s. Therefore one can model the reaction system as a plane with substrate molecules covalently anchored to it and enzyme molecules sliding (or rolling) across it. Each time an enzyme (E) molecule encounters a substrate (F), an adduct (EF) is formed. This adduct does not generally
The rate constant for the chemical step on the surface is denoted k c to distinguish it from the corresponding parameter in solution (k cat). Overall, we have the two-step kinetic model outlined in Scheme 1. We implicitly assume that we can combine diffusion and orientation into a single step leading to the formation of a reactive complex. These rate processes can be described by the following set of equations: d@EF*# 5 k o@E#@F# 2 k c @EF*# dt
[4]
d@F# 5 2k o@E#@F# dt
[5]
d@P# 5 k c @EF*# dt
[6]
@F# 1 @EF*# 1 @P# 5 F 0
(substrate balance)
[7]
In general they lead to a complex kinetic solution. Simplification results by assuming that the rate of formation of the active complex is very different from the rate of the chemical cleavage step, so that the free enzyme concentration [E], and hence the active complex concentration [EF*], are approximately constant. Given this assumption, Eqs. [4] to [7] reduce to d@P# 5 k o@E#~F o 2 @P#! dt d@P# 5 k c ~F o 2 @P#! dt
k c @ k o@E#
k o@E# @ k c .
[8]
[9]
Integrating Eqs. [8] and [9] gives P 5 F o~1 2 e 2k o@E#t ! P 5 F o~1 2 e 2k ct !
k c @ k o@E# k o@E# @ k c .
[10] [11]
Equations [10] and [11] correspond to a pseudo first and a first-order reaction rate, respectively. To verify these relations we fit the experimental data with a first-order exponential, as shown in Figs. 3a, 3b, and 4, the
85
ENZYME KINETICS AT SURFACES
latter being previously published experimental results (1). The semilog plots for Figs. 3a and 3b are shown in Fig. 5. The reactions follow first (or pseudo first)-order kinetics. These results confirm the assumption that one of the two steps is much slower than the other while still not discriminating between the two cases. The rate-limiting step must either be the chemical one (hydrolysis of the EF* complex) or the diffusion/orientational step (formation of the EF* complex). To discriminate between these possibilities, we conducted a series of experiments at a lower pH. Collagenase activity in the bulk (as expressed by k cat) is maximal at pH 7.5 and decreases about 3-fold at pH 6 (2). The data from our experiments (Fig. 3), however, together with the model overlay (Fig. 5), show an increase (3- to 4-fold) rather than a decrease in reaction rate at pH 6.05. This suggests that enzymatic cleavage is not the rate-limiting step and that the formation rate of the enzyme complex is enhanced at lower pHs. While it is possible that the dependence of enzyme activity on pH may be different on a surface than it is in solution, the decrease in the observed overall rate with respect to the bulk or solution k cat (about 5 3 10 5-fold) strongly suggests that the slow step is qualitatively different in this case. Results from two previous studies support this conclusion. First, Sandwick and Schray (4) demonstrated that enzymes adsorbed to surfaces at high concentrations retain a significant fraction of their solution activity. In our experiments, the enzyme is adsorbed at saturating levels and surface concentration is as high as it can become. Second, with respect to the effect of pH on enzyme activity, Russell and Fersht (5) showed that at low ionic strengths (,100 mM) there was indeed a measurable dependence. At higher ionic strengths such as the ones used in this study (.500 mM), however, this dependence all but disappeared. This is thought to be due to electrostatic screening of the active site. Previously reported results using surface-bound substrates (1) also show increases in the overall reaction rate at low pH (Fig. 6). The influence of pH on enzymatic activity at surfaces is complex due to the changing structure of the protein and the substrate due to the
FIG. 5. Semilogarithmic plots of the FALGPA hydrolysis reactions shown in Fig. 3.
FIG. 6. Previously reported (1) results of FALGPA/collagenase reactions at low pH. First-order fit curves are overlaid (dashed lines).
titration of ionizable groups. The isoelectric point (pI) of collagenase A is 8.6 (6) and it contains 16 histidines, each having a pI of 6.0. The charge of the quartz surface is unlikely to change at pH 6 as the surface silicates have a pI lower than 4. The cleavage product of FALGPA has a terminal amino group whose pK is greater than 8, and thus it is protonated at both pH 6 and pH 7. It is likely that the observed changes occur because of a decrease in energy of the weak bonds that restrict the overall enzyme mobility (both translational and orientational) due to titration of charged moieties on the enzyme molecule. The kinetic data allow some inference about the nature of the enzyme-surface bonds. The overall rate constant k at pH 7.5 measured from the plots (Figs. 3a and 5) corresponds to k o[E] in our model and is equal to 3.3 3 10 25 s 21. This implies an initial enzyme turnover rate of d@F# U @E#dt U
5
k o@E#@F O# @E#
5
~3.3 3 10 25 ! 3 ~2 3 10 210 ! 5 0.002 s 21. 4 3 10 212
t50
The corresponding value of the initial enzyme turnover rate at pH 6.05 is larger but on the same order of magnitude. By assuming that the mean free path of an enzyme molecule is the average distance between substrates, around 14 Å (1), and by knowing the 2D diffusion coefficient (3), we can estimate a frequency of EF encounters of 10 5/s per molecule. It is apparent that the majority of encounters have a consistently unfavorable orientation to react, and this suggests that the enzyme is restrained in its orientation as it moves along the surface (7). Put in another way, the conformation that minimizes the adsorption free energy is not favorable for substrate binding; hence, most of the complexes formed are unreactive. It would be interesting to have the 3D structure of collage-
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TRIGIANTE, GAST, AND ROBERTSON
nase available so as to propose hypotheses about the nature of the enzyme/peptide contact orientation, but unfortunately it is not known at this time (8).
ing. The reaction is therefore diffusion and/or orientation controlled and from the value of the rate constant the conclusion can be drawn that the enzyme/derivatized surface bond may involve a preferred, nonrandom orientation of the enzyme.
SUMMARY
The reaction between adsorbed Clostridium collagenase and the covalently surface bound model substrate FALGPA displays pseudo first-order kinetic behavior. A two-step model is developed to describe the reaction, consisting of a diffusioncontrolled process in which the reactants form a complex capable of chemically reacting, followed by a chemical cleavage step. The first- or pseudo first-order nature of the observed kinetics suggests that one of the two steps is rate-limiting. The substantial decline in the reaction rate, together with a pH dependence that is reversed with respect to that in solution, indicate that the chemical cleavage step is not rate-determin-
REFERENCES 1. Gaspers, P., Gast, A. P., and Robertson, C. R., J. Colloid Interface Sci. 172, 518 (1995). 2. van Wart, H. E., and Steinbrink, R., Anal. Biochem. 113, 356 (1981). 3. Gaspers, P., Gast, A. P., and Robertson, C. R., Langmuir 10, 2699 (1994). 4. Sandwick, R. K., and Schray, K. J., J. Colloid Interface Sci. 121, 1 (1988). 5. Russell, A. J., and Fersht, A. R., Nature 328, No. 6, 496 (1987). 6. Nordwig, A., Leder 13, 10 (1962). 7. Robeson, J. L., and Tilton, R. D., Langmuir 12, 6104 (1996). 8. Matsushita, O., Chang-Min, J., Minami, J., Katayama, S., Nishi, N., and Okabe, A., J. Biol. Chem. 273, No. 6, 3643 (1998).