Determination of Interaction Kinetic Constants for HIV-1 Protease Inhibitors Using Optical Biosensor Technology

Analytical Biochemistry 291, 207–218 (2001) doi:10.1006/abio.2001.5025, available online at http://www.idealibrary.com on

Determination of Interaction Kinetic Constants for HIV-1 Protease Inhibitors Using Optical Biosensor Technology 1 Per-Olof Markgren,* Maria T. Lindgren,* Karl Gertow,* Robert Karlsson,† Markku Ha¨ma¨la¨inen,† and U. Helena Danielson* ,2 *Department of Biochemistry, Uppsala University, BMC, Box 576, S-751 23 Uppsala, Sweden; and †Biacore AB, S-754 50 Uppsala, Sweden

Received June 27, 2000; published online March 9, 2001

The interaction between HIV-1 protease and inhibitors has been studied with optical biosensor technology. Optimized experimental procedures and mathematical analysis permitted determination of association and dissociation rate constants. A sensor surface with native enzyme was unstable and exhibited a drift that was influenced by the binding of inhibitor. This was hypothesized to be due to a specific mechanism involving autoproteolysis and/or dimer dissociation. The use of a mutant predicted to be less susceptible to autoproteolysis (Q7K) than wild-type enzyme resulted in a minor effect on surface stability, while a completely stable surface was obtained by treatment of the immobilized enzyme with N-ethyl-Nⴕ-(dimethylaminopropyl)-carbodiimide and N-hydroxysuccinimide; the most stable surface was achieved by chemically modifying the Q7K enzyme. The stabilized surface was enzymatically active and the interaction with inhibitors was similar to that for native enzyme. Several of the inhibitors had very high association rates, and estimation of kinetic constants was therefore performed with a binding equation accounting for limited mass transport. Of the clinical inhibitors studied, saquinavir had the highest affinity for the enzyme, a result of the lowest dissociation rate. Although the dissociation rate for ritonavir was sixfold faster, the affinity was only twofold lower than that for saquinavir since the association rate was threefold faster. Nelfinavir and indinavir exhibited lower affinities relative to the other inhibitors, a consequence of a slower association for nelfinavir and a relatively fast dissociation for indinavir. These results show that biosensor-based interaction studies can resolve affinity into

1

This work was supported by the Swedish National Board for Industrial and Technical Development (NUTEK) and Medivir AB, Huddinge, Sweden. 2 To whom correspondence should be addressed. Fax: ⫹46-18550733. E-mail: [email protected]. 0003-2697/01 $35.00 Copyright © 2001 by Academic Press All rights of reproduction in any form reserved.

association and dissociation rates, and that these are characteristic parameters for the interaction between enzymes and inhibitors. © 2001 Academic Press Key Words: HIV; protease; inhibitor; indinavir; nelfinavir; ritonavir; saquinavir; interaction; binding; affinity; inhibition; association; dissociation; biosensor; Biacore; mass transport; surface plasmon resonance (SPR).

The development of inhibitors toward HIV-1 protease has proved to be an example of successful rational drug development, in that detailed structural and functional information about the target enzyme, the inhibitors, and their interaction has been used throughout the development process (1). Although HIV-1 protease inhibitors are now used with great efficiency in clinical treatment of AIDS and improve the life quality and survival of HIV-infected patients, there are serious side effects and limitations to their use. To design and evaluate optimized drugs it is essential to be able to analyze the interaction between the inhibitors and the target enzyme in detail. However, the most potent inhibitors have reached the limit of available enzyme inhibition assays and structure– activity analysis is therefore essentially limited to static structural studies of enzyme–inhibitor complexes. Such complexes do not reveal the kinetics of the interaction, i.e., the association and dissociation rates, or the ratio of these parameters, the affinity. Consequently, little is known about the kinetics of the interactions for different inhibitors and their importance for the clinical efficacy of inhibitors. In previous investigations we have studied the interaction between HIV-1 protease and various lowmolecular-weight inhibitors with a surface plasmon 207

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resonance (SPR) 3 -based biosensor (2, 3). Determination of association and dissociation rate constants for the inhibitors was prevented by an instability of the immobilized enzyme resulting in a signal drift (3). Since the binding of an inhibitor influenced the drift, it was not possible to evaluate the sensorgrams with an equation only accounting for a linear time-dependent drift term (a standard correction procedure). To overcome the limitations in the analysis caused by the drift, it was necessary to understand the mechanism so that a suitable mathematical analysis could be performed, or, preferably, to find methods that could stabilize the surface. It was hypothesized that the drift was caused by dissociation of dimers or by autoproteolysis (or both). In either case, noncovalently bound fragments or monomers would be washed away from the surface, resulting in a reduced signal and loss of binding capacity. Since inhibitors may stabilize the dimer (4, 5) and prevent proteolysis, both hypotheses are consistent with the effect of inhibitors on the drift. In the present study, different approaches have been applied to elucidate the drift mechanism, to obtain a stable surface, and to identify suitable equations that describe the interaction and can be used for determination of kinetic constants. In addition, the capacity of the buffer flow and the diffusion to transport analyte to and from the sensor surface was evaluated by including transport rate constants in the equations (6). The observed association and dissociation rates are reduced when the transport rate is slower or of the same order as the rates of the interaction itself, since the concentration of free inhibitor is reduced close to the sensor surface during association and increased during dissociation. It was previously found that the interaction kinetics for a series of HIV-1 protease inhibitors differed significantly (3). Although initial estimates of affinity and dissociation rates were based on experimentally defined parameters, binding affinity estimated from biosensor analysis was shown to be correlated with inhibition constants for the inhibitors (K i ). In contrast, the dissociation rates did not correlate with K i values, indicating that the interaction kinetics obtained by biosensor analysis were characteristic for different inhibitors and that they could not be predicted by enzyme inhibition studies. The association and dissociation rate constants determined by the present method provide additional support for these conclusions. 3

Abbreviations used: SPR, surface plasmon resonance; DMSO, dimethyl sulfoxide; EDC, N-ethyl-N⬘-(dimethylaminopropyl)-carbodiimide; NHS, N-hydroxysuccinimide; RFU, relative fluorescence units.

MATERIALS AND METHODS

Enzyme and Inhibitors The plasmid containing the wild-type HIV-1 protease gene (Lindgren et al., submitted) was used as a template for cloning of the Q7K mutant, using procedures as described by Maniatis et al. (7). Mutagenesis, expression, and purification were performed as described elsewhere (Lindgren et al., submitted). Saquinavir was from Roche Registration Ltd. (Hertfordshire, UK), ritonavir was from Abbott Laboratories Ltd. (Kent, UK), nelfinavir was from Agouron Pharmaceuticals Inc. (La Jolla, CA), and indinavir was from Merck Sharp & Dohme Ltd. (Hertfordshire, UK). Inhibitors B268 and B376 were compounds 28 and 41 as described by Alterman et al. (8), while inhibitor B365 was compound 4 in Wachtmeister et al. (9). Stock solutions of inhibitors were made up to 1–10 mg/ml in DMSO and stored at ⫺20°C. Biosensor Measurements Measurements were performed with a Biacore 3000 instrument (Biacore AB, Uppsala, Sweden), thermostated at 20°C. The running buffer was 0.01 M Hepes, pH 7.4, 0.15 M NaCl, 3 mM EDTA, 0.005% (v/v) Tween 20 (HBS-EP, Biacore AB, Uppsala, Sweden) with the addition of 3% DMSO used at flow rates of 20 or 40 ␮l/min. The sensor surface was regenerated between sample injections by injection of 100% ethylene glycol and the flow system was washed with 50% DMSO in HBS-EP and 0.01% Tween 20. A buffer blank was injected to detect possible carryover between samples. A reference flow cell without enzyme was used to correct for differences in bulk refractive index between sample and running buffer, although such differences were carefully minimized during sample preparation. The sensorgrams obtained on surfaces with negligible drift (stabilized Q7K surfaces) were further corrected by subtraction of an average blank sensorgram obtained by averaging sensorgrams from buffer injections distributed over the series of injections in a certain experiment (10). Immobilization and Stabilization Procedures About 2000 RU of HIV-protease was normally immobilized on a CM5 sensor chip (Biacore AB) by amine coupling using N-ethyl-N⬘-(dimethylaminopropyl)-carbodiimide (EDC) and N-hydroxysuccinimide (NHS) as previously described (2). When indicated, the immobilized HIV-1 protease was stabilized by treatment with a fresh mixture of EDC and NHS (0.2 and 0.05 M, respectively) during a 7-min injection. The surface was then left for a spontaneous deactivation for at least 30 min before being used for analysis. By applying the stabilization procedure in only one of the two flow cells

INTERACTION KINETICS FOR HIV-1 PROTEASE INHIBITORS

with immobilized enzyme, it was possible to compare the binding of inhibitors on stabilized and unstabilized surfaces in the same experiment.

关AB兴 ⫹ 关B兴 ⫽ R max

[10]

The BIAevaluation software version 3.0.2 (Biacore AB) was used for evaluation of sensorgrams. The complete sensorgrams (association and dissociation phases) for a series of concentrations were analyzed simultaneously by global fitting. New mathematical models accounting for the observed analyte-influenced drift and mass transport effects were defined. Model 1: Langmuir binding with analyte influenced drift

d关B兴/dt ⫽ ⫺d关AB兴/dt 关AB兴 ⫹ 关B兴 ⫽ R max.

d关AB兴/dt ⫽ k t共关A0 兴 ⫺ K D关AB兴/关B兴兲

[2] [3] [4]

[5]

This expression is based on the experimental results presented in Fig. 1B. [A 0] is the concentration of injected analyte, S 0 is the drift in the absence of inhibitor, R max is the response that corresponds to saturation of the immobilized enzyme (maximal binding signal), and RI is a correction for bulk refractive index. An analytical solution to this equation system is described in Appendix 1. By introducing a mass transport coefficient, k t (6), this model was extended to also correct for changes in analyte concentration at the sensor surface under mass transport limiting conditions. Model 2: Langmuir binding limited by mass transport combined with analyte influenced drift Total response ⫽ 关AB兴 ⫹ D ⫹ RI

[6]

[AB] is here defined by the following four equations: d关AB兴/dt ⫽ k a关A兴关B兴 ⫺ k d关AB兴 d关B兴/dt ⫽ ⫺d关AB兴/dt

Total response ⫽ 关AB兴 ⫹ RI

[11]

[AB] is defined by the following three equations:

D is the drift term and defined by: dD/dt ⫽ S 0 共1 ⫺ 关AB兴/R max兲.

The drift term D is defined as in Model 1 (Eq. [5]). For evaluation of the degree of limitation in transport, a model where mass transport completely limits the interaction rates was applied (11). Model 3: Langmuir binding with completely transport limited interaction

[1]

[AB] is defined by the following three equations: d关AB兴/dt ⫽ k a关A0 兴关B兴 ⫺ k d关AB兴

[9]

d关A兴/dt ⫽ k t共关A0 兴 ⫺ 关A兴兲 ⫺ 共k a关A兴关B兴 ⫺ k d关AB兴兲.

Nonlinear Regression Analysis

Total response ⫽ 关AB兴 ⫹ D ⫹ RI

209

[7] [8]

d关B兴/dt ⫽ ⫺d关AB兴/dt 关AB兴 ⫹ 关B兴 ⫽ R max.

[12] [13] [14]

This model is a complement to the kinetic transport model and describes the situation where k a*R max Ⰷ k t. Under such circumstances, the kinetic information is lost but it is still possible to determine the affinity (K D) of an interaction. Appendix 2 describes the corresponding equations as entered in the “Fit general” module in BIAevaluation software. The models for 1:1 Langmuir binding with and without mass transport limitations as defined in the BIAevaluation software were also used. Enzyme Activity and Stability Measurements The enzymatic activity of immobilized HIV-1 protease was measured essentially as in the standard activity assay previously described (12). Both the immobilization and the substrate hydrolysis reactions were performed directly on the whole chip surface (7 ⫻ 7 mm 2) (outside the biosensor instrument) at room temperature. Fifty microliters of 5 ␮M HIV-1 protease substrate M-1865 (Bachem, Bubendorf, Switzerland), in 100 mM acetate buffer, pH 5.0, with 1 M NaCl and 2.7% DMSO, was applied to sensor chips with immobilized Q7K mutant with and without previous treatment with EDC/NHS. The experiment included a positive control with approximately 30 ng enzyme added in solution and a negative control without enzyme. The samples were analyzed by measuring the fluorescence in relative fluorescence units (RFU) after 30 min of incubation with a Fluoroskan plate reader (Labsystems, Helsinki, Finland). The presented fluorescence values are based on triplicates.

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to exaggerate the drift in this experiment by using a fresh surface with a high immobilization level. No drift was observed at high concentrations of inhibitor, when the enzyme was essentially saturated with inhibitor (Fig. 1A). In addition, after dissociation of the inhibitor, the baseline continued from the same level as it had when the inhibitor was injected, indicating that the surface was stabilized during the time inhibitor was bound. The effect was dependent on the amount of bound inhibitor as shown by the linear relationship (R 2 ⫽ 0.96) between the extent of the drift (i.e., the slope) and the binding response, at the steady-state binding level for different concentrations of inhibitor (Fig. 1B). Kinetic Analysis of Interaction with Unstabilized Surface Different mathematical models were evaluated for describing sensorgrams with analyte-influenced drift by using global nonlinear regression analysis. An expression for the drift during an injection was derived on the basis of the proportionality between relative binding and relative drift (Fig. 1B): S共t兲/S 0 ⫽ 1 ⫺ AB共t兲/ABmax. FIG. 1. (A) Influence of inhibitor on sensor surface stability. Sensorgrams for 0 –100 ␮M B365 using 7000 RU of HIV-1 protease without chemical stabilization. The sensorgrams are averages of three measurements. (B) Relative slope at steady-state binding level vs relative binding level (cf. Eq. [1]).

To investigate the stability of the wt and Q7K enzymes, samples of the enzymes were incubated at room temperature for 24 h. Aliquots were taken at 0, 1, 4, 7, and 24 h and subjected to SDS–PAGE using highdensity Phast gels and silver staining according to standard protocols (Amersham-Pharmacia Biotech, Uppsala, Sweden). In addition, wt and Q7K enzymes (7– 8 ␮g/ml) were incubated in 100 mM acetate buffer, pH 5.0, with 1 M NaCl and 2.7% DMSO at 37°C for 15 min to 6 h. Aliquots to final concentration of 0.25 ␮g/ml were taken for initial activity measurements with continuous fluorescence detection in the same buffer containing 5 ␮M HIV-1 protease substrate M-1865 (as above). The presented activity values are based on four replicates.

[15]

In this equation, S(t) is the analyte-influenced drift at a certain binding level AB(t) of an inhibitor, S 0 is the drift in the absence of inhibitor, and AB max is the maximal binding level corresponding to saturation of the sensor surface (Model 1 and Appendix 1). The properties of the derived model were tested theoretically as follows. Sensorgrams representing injection of different concentrations of inhibitor to a surface displaying analyte-influenced drift were simulated with the BIAevaluation software according to the integrated equations in Appendix 1 (Fig. 2). The simulated sensorgrams showed the same general features as seen experimentally in Fig. 1, a decrease in drift with in-

RESULTS

Influence of Inhibitor on Sensor Surface Stability Long injections (200 s) of different concentrations of a quickly associating and dissociating inhibitor (B365) revealed that the binding of the inhibitor to the enzyme surface reduces the signal drift (Fig. 1). It was possible

FIG. 2. Simulated sensorgram with analyte-influenced drift 0 –10 ␮M, k on ⫽ 100,000 M ⫺1 s ⫺1, k off ⫽ 0.1 s ⫺1.

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K D ⫽ 0.9 nM, R max ⫽ 42 RU, ␹ 2 ⫽ 0.5 RU 2; and Day 2 (Fig. 4C): k on ⫽ 2.6 ⫻ 10 6 M ⫺1 s ⫺1, k off ⫽ 2.6 ⫻ 10 ⫺3 s ⫺1, K D ⫽ 1.0 nM, R max ⫽ 26 RU, ␹ 2 ⫽ 0.3 RU 2.

FIG. 3. Sensorgrams for binding of 5 nM indinavir to HIV-1 protease at flow rates 15, 40, and 75 ␮l/min.

creased binding, and a corresponding shift in baseline level after dissociation. By fitting the equation to simulated sensorgrams (with added noise) using numerical integration (Model 1), it was confirmed that the model could converge to a unique set of parameters as long as reasonable starting estimates were provided and that the two mathematical representations of the model were equivalent. Considering the high association rates, we investigated the influence of mass transport on the interaction; sensorgrams for an injection of 5 nM indinavir were recorded at three different flow rates: 15, 40, and 75 ␮l/min. The observed association rate increased with increasing flow rate (Fig. 3). Sensorgrams under the same conditions for saquinavir, ritonavir, and nelfinavir were similar. Subsequent experiments were therefore performed at the highest flow rate that was practical, and analysis of sensorgrams included a separate term for the transport rate constant (see below). Global fitting of the derived equation describing analyte influenced drift to a series of sensorgrams for B268 and indinavir are presented in Fig. 4. The equation with analyte influenced drift (Model 1) could describe the binding of B268 to immobilized HIV-1 protease (Fig. 4A, k on ⫽ 8.8 ⫻ 10 4 M ⫺1 s ⫺1; k off ⫽ 3.3 ⫻ 10 ⫺3 s ⫺1; K D ⫽ 37.5 nM; R max ⫽ 35 RU; ␹ 2 ⫽ 0.2 RU 2). In contrast, binding of indinavir was not well described by this model since it was influenced by transport effects (compare Fig. 3). However, by analyzing these data with the kinetic transport model, a reasonable fit was obtained (Figs. 4B and 4C, Model 2). The parameters calculated from the data presented in Figs. 4B and 4C were obtained assuming a global R max for each data set, while the drift and refractive index offset were obtained as unique parameters for each binding curve. The kinetic parameters did not change from one day to the next, despite the slow dissociation of the enzyme from the surface and a resulting reduction of binding capacity. The same surface was used for determination of kinetic parameters on two consecutive days: Day 1 (Fig. 4B): k on ⫽ 2.8 ⫻ 10 6 M ⫺1 s ⫺1, k off ⫽ 2.6 ⫻ 10 ⫺3 s ⫺1,

FIG. 4. Interaction between BEA-268 1–160 nM (A), indinavir 3.13–100 nM (B), and indinavir 3.12–50 nM (C) and unstabilized wild-type HIV-1 protease. Sensorgrams were fitted to Model 1 (BEA268) and Model 2 (indinavir).

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and the binding capacity. The Q7K mutant lost 47% of the binding capacity and the wild-type enzyme lost 66%, while the chemically stabilized enzymes only lost 11 and 24%, respectively. The enzyme was enzymatically active after immobilization and chemical stabilization. The amount of product formed by stabilized and by unmodified enzyme was not significantly different (3.39 ⫾ 0.16 and 3.57 ⫾ 0.21 RFU, respectively, ⫾ standard error based on three replicates). By repeating the activity measurement on the same surfaces 4 days later (wet storage at 8°C), it was shown that the stabilization procedure also preserves the enzymatic activity (3.57 ⫾ 0.15 RFU), in addition to the immobilization level and inhibitor binding capacity. During the 4 days the activity of the unstabilized enzyme decreased by 59% to 1.48 ⫾ 0.18 RFU. The positive control of 30 ng HIV-1 protease produced a fluorescence of 2.0 RFU. The activity of the immobilized enzyme yielding about 3.5 RFU thus corresponds to about 50 ng enzyme with the same specific activity as in the original stock solution. On the 7 ⫻ 7-mm 2 sensor surface this corresponds to 1000 pg/mm 2 or about 1000 RU. FIG. 5. Effect of chemical stabilization and substitution of Gln-7 by Lys (A) immobilized protein vs time, (B) binding capacity vs time. }, wild type without stabilization; ■, wild type with stabilization; Œ, Q7K without stabilization; ⫻, Q7K with stabilization.

Stabilization of the Sensor Surface The initial strategy to stabilize the enzyme was to substitute Glu-7 by Lys. The catalytic properties of the mutant were similar to those of the wild-type enzyme (k cat /K M ⫽ 1.5 ⫾ 2.0 and 0.52 ␮M ⫺1 s ⫺1 respectively), while the k cat value was 29 ⫾ 9 s ⫺1 and the K M value was 20 ⫾ 25 ␮M compared to 7.3 s ⫺1 and 14 ␮M for the wild-type enzyme. However, it was confirmed that the Q7K enzyme did not show any degradation even after 24 h, while the wild-type enzyme was partially degraded after 7 h (data not shown). In addition, both enzyme forms lost most of their activity within 6 h incubation, the decrease being ⫺89 ⫾ 4% for the Q7K and ⫺98 ⫾ 2% for the wild-type enzyme. After 1 h the decrease in activity of the Q7K mutant was ⫺54 ⫾ 9%, while that for the wild-type enzyme was ⫺79 ⫾ 6%. Further stabilization was achieved by treating the immobilized enzyme with a mixture of EDC/NHS. The chemically modified surface showed an almost constant baseline level after 105 h for both enzyme forms (Fig. 5A). Repeated injections of 100 nM indinavir revealed that the binding capacity was also retained during the same time period (Fig. 5B). The Q7K enzyme surface was slightly more stable than the wild type, as judged by the amount of enzyme on the chip

Kinetic Analysis of Interaction with Stabilized Surface The association and dissociation rate constants could be determined for the interaction between B376 and the chemically stabilized Q7K enzyme, evaluated without accounting for the baseline drift: k on ⫽ 4.32 ⫾ 0.01 ⫻ 10 5 M ⫺1 s ⫺1 ; k off ⫽ 8.39 ⫾ 0.02 ⫻ 10 ⫺3 s ⫺1 ; K D ⫽ 19.4 nM (⫾standard error from BIA evaluation software). In comparison, the parameters for B376 and the unstabilized Q7K enzyme evaluated with interaction-influenced drift were k on ⫽ 3.30 ⫾ 0.01 ⫻ 10 5 M ⫺1 s ⫺1 , k off ⫽ 6.58 ⫾ 0.01 ⫻ 10 ⫺3 s ⫺1 , and K D ⫽ 19.9 nM. The association and dissociation rate constants for the clinically used HIV-1 protease inhibitors indinavir, saquinavir, ritonavir, and nelfinavir were determined with the chemically stabilized Q7K surface (Table 1). For these measurements the influence of transport limitation was minimized by using a low immobilization level (ca. 2000 RU) and a high flow rate (40 ␮l/min). In addition, nonlinear regression analysis of sensorgrams (Fig. 6) was performed with an equation that included an expression for limited mass transport (“1:1 binding with mass transfer” in BIAevaluation software). Analysis of Mass Transport The average transport rate constants, k t (Table 1), indicate that ritonavir is the only inhibitor to show a significant transport limitation, since the other transport rate constants are large and undetermined (large

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INTERACTION KINETICS FOR HIV-1 PROTEASE INHIBITORS TABLE 1

Interaction Kinetic Constants for HIV-1 Protease Inhibitors k on (M ⫺1 s ⫺1) Indinavir Ritonavir Nelfinavir Saquinavir

1.40 2.45 6.63 8.19

⫻ ⫻ ⫻ ⫻

10 6 10 6 10 5 10 5

⫾ ⫾ ⫾ ⫾

2.9 ⫻ 10 5 2.1 ⫻ 10 5 2.18 ⫻ 10 5 1.37 ⫻ 10 5

k off (s ⫺1) 1.60 1.71 7.97 2.77

⫻ ⫻ ⫻ ⫻

10 ⫺3 10 ⫺3 10 ⫺4 10 ⫺4

⫾ ⫾ ⫾ ⫾

9 ⫻ 10 ⫺5 1.2 ⫻ 10 ⫺4 10 ⫺5 2.0 ⫻ 10 ⫺5

k t (RU M ⫺1 s ⫺1)

K D (nM) 1.15 0.70 1.20 0.34

⫾ ⫾ ⫾ ⫾

0.24 0.08 0.41 0.06

3.4 2.6 2.0 8.7

⫻ ⫻ ⫻ ⫻

10 18 10 7 10 20 10 16

⫾ ⫾ ⫾ ⫾

3.3 ⫻ 10 18 2 ⫻ 10 6 2.0 ⫻ 10 20 8.7 ⫻ 10 16

Note. The sensor surface was a chemically stabilized Q7K mutant and parameters were estimated by global fit of an equation describing 1:1 binding with mass transfer. (⫾SE based on four replicates).

errors). However, the variations between individual measurements were large. The recorded sensorgrams were also analyzed with two alternative equations representing the extreme cases of the kinetic transport model (BIAevaluation software: “1:1 binding with mass transfer”). The first case is when association and dissociation rates are governed only by the interaction between enzyme and inhibitor (BIAevaluation software: “1:1 (Langmuir)

binding”) and the second when they are governed only by the transport capacity of the buffer flow and the diffusion (Model 3) (11). In the latter case the affinity can be determined but not the kinetic parameters. Better fits were achieved for the clinical inhibitors with the kinetic transport model than with the “only interaction” model. However, the “only transport” model failed to accurately describe interaction curves and gave larger residuals than those obtained when data

FIG. 6. Sensorgrams for binding of saquinavir, ritonavir, indinavir, and nelfinavir to HIV-1 protease evaluated with an equation accounting for limited mass transport.

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FIG. 7. (A) Binding of 0 – 40 nM indinavir to stabilized HIV-1 protease. Residuals for (B) kinetic model, (C) kinetic transport model, and (D) affinity transport model.

were analyzed with the kinetic transport model (Fig. 7). DISCUSSION

We have previously used the surface plasmon resonance biosensor for the detection of compounds that interact with HIV-1 protease (2) and for estimation of affinities and dissociation rates (3). Due to the instability of the enzyme, experimentally defined estimates of affinity and dissociation rate were used instead of the theoretically defined rate constant. In this way a correlation between affinity and inhibition constants (obtained from enzyme activity inhibition measurements) was demonstrated, strongly supporting that the biosensor results reflects the properties of an active site interaction. To overcome the problems with the instability of the sensor surface and to be able to estimate the kinetic constants, two different approaches were applied in the present investigation. The initial approach was mathematical and based on the derivation of an equation that described the influence of the analyte on the stability of the surface. This model was then used for nonlinear regression analysis of the experimental data. The new model was found to describe sensorgrams recorded with HIV-1 protease on the sensor surface well. A further improvement was observed when mass transport effects were included in the model, especially for indinavir that has a high association rate constant and thus a stronger tendency to show mass transport limited interaction. The practical usefulness of this mathematical approach was limited due to the continuous change in drift and binding capacity over time. These parameters had to be fitted locally to each curve

since they were time dependent and varied between injection cycles. The variation in drift also prevents the subtraction of the signal from a blank injection to remove systematic disturbances during injections. However, the new models offer an improved possibility to describe and evaluate sensorgrams from systems where an analyte-affected drift is observed and a stable surface cannot be obtained. An experimental approach for dealing with the drift was also taken, where the aim was to stabilize the surface. The observation that there was a correlation between the stability of the surface and the binding of inhibitor was consistent with autoproteolysis or dimer dissociation as major causes for the drift. The hypothesis involving autoproteolysis was addressed by constructing a mutant where Gln-7 was substituted by Lys, reducing hydrolysis of the bond between Leu-5 and Trp-6 (13). We found that the Q7K-mutant surface was only slightly more stable than the wild-type enzyme surface, indicating that autoproteolysis is not the primary cause for the surface instability. A second strategy for stabilizing the sensor surface was based on the accidental discovery that treatment of the immobilized enzyme with EDC and NHS resulted in an essentially permanent surface with constant binding capacity. This procedure is used for the activation of carboxyl groups in the immobilization matrix to establish a covalent link between these groups and primary amines of the protein to be immobilized. Since the efficiency of immobilization is limited, the surface will contain subunits and dimers that are not covalently bound and by repeating the immobilization procedure a greater proportion of protein will be covalently attached to the surface. However, the

INTERACTION KINETICS FOR HIV-1 PROTEASE INHIBITORS

second treatment may also activate carboxyl groups in the protein whereby reaction with primary amines (also in the protein) can result in intra- and intermolecular cross-links. Intermolecularly cross-linking monomers or dimers that were not covalently fixed to the matrix would enhance the stability of the surface. These results indicate that dissociation of noncovalently bound monomers is the most important factor for surface instability. The immobilization procedure is reasonably mild for the enzyme as judged by the activity of the immobilized HIV-1 protease. In addition, the kinetic properties of the chemically modified enzyme were very similar to those of the native enzyme, indicating that the procedure did not interfere with the enzyme interaction with inhibitors. These results support that the immobilized and stabilized protein structurally and functionally corresponds to native HIV-1 protease. Consequently, the method for chemical stabilization of the immobilized enzyme clearly provides a possibility of evaluating the kinetics of the interaction between HIV-1 protease with inhibitors. Since maximal stability was achieved by chemical modification of the Q7K mutant, this enzyme form was used for estimation of the kinetic parameters for inhibitors. In the present study, the effects of transport on the observed association and dissociation rates were indicated in three different ways in the results. First, for some inhibitors the association rate was affected by the flow rate during the injection. Second, a mathematical model that accounted for limited mass transport resulted in improved fit compared with one only accounting for the interaction. However, a model assuming complete transport limitation did not describe the sensorgrams well, thus indicating that the sensorgrams contained significant information about the intrinsic rates of the interaction. Finally, the transport rate constants that were determined in the nonlinear regression indicate limited transport when they are low compared with the association rate constant and the binding capacity of the surface. When the transport rate is not limiting and does not give a significant contribution to the shape of the curves fitted to the sensorgrams, the transport rate constant is not well determined, i.e., has large errors, and the mass transport term does not influence the determination of the interaction rate constants (14). However, these different estimates of a limited transport gave different results and the variations between individual measurements were large. For example, the results from the flow rate experiment suggest that transport is severely limited for all of the clinical inhibitors. The nonlinear regression with equations for different levels of transport limitation (none/moderate/complete) indicated a moderate transport limitation for about half of the measurements and a severe limitation for only one of

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them and the transport rate constants gave similar results. The interaction that was clearly limited by transport was ritonavir, the inhibitor with the highest association rate constant. This indicates that the present method is limited only for very rapidly associating compounds. Use of a high flow rate and, more importantly, reduction of the amount of immobilized HIV-1 protease on the sensor surface minimized but did not fully eliminate the limitation in transport. Consequently, to obtain an acceptable fit for inhibitors with high association rates, it was necessary to use an equation taking transport limitation into account. However, also other, so far unknown, disturbances seem to affect the results to some extent since not all of the deviations from the simple 1:1 Langmuir model could be explained according to the theory for transport limitation. The association and dissociation rates for the clinical HIV-1 protease inhibitors were found to be significantly different. Of these compounds, saquinavir exhibits the highest affinity, a result of a particularly slow dissociation relative to the other inhibitors, in spite of a slow association. Although ritonavir displays the fastest dissociation, the equilibrium affinity is not much lower than that for saquinavir since it has a high association rate. Indinavir and nelfinavir have similar and lower affinities but indinavir is characterized by a quick dissociation, while nelfinavir has a particularly slow association. The equilibrium affinity and either of the rate constants are not individually correlated. However, there may be correlation between the association and dissociation rate constants, such that fast association is coupled to fast dissociation and vice versa. Recent studies of the kinetics of the antiviral efficiency of HIV-1 protease inhibitors in infected human cells in culture (15) support the hypothesis that association or dissociation rates may be of pharmacokinetic/pharmacodynamic importance. The rates of recovery of infectivity after interrupted protease treatment correlated with the dissociation rate constant for three of the four inhibitors tested. With the observed half-time for the dissociation (t 1/ 2,obs) previously determined (3) there was a correlation for all four of the clinical inhibitors. Although Nascimbeni et al. conclude that the differences in antiviral kinetics appear to be due to differences in the intracellular concentration and/or rates of cellular clearance, the correlation is an interesting observation that deserves further study. The present study illustrates that by optimizing the experimental procedures and the mathematical analysis it was possible to determine interaction kinetic constants for low-molecular-weight inhibitors of HIV-1 protease. In the context of drug discovery, the described method contributes by offering a better resolu-

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tion in affinity between inhibitors with very high affinity compared with enzyme activity inhibition assays. Clearly the method also offers an improved resolution between inhibitors with the same equilibrium affinity but different rates of association and dissociation, opening up for structural and mechanistic interpretations from studies of series of candidate drugs and mutant enzymes.

The expression for the binding level in the association phase is B ass共t兲 ⫽ B max共关I兴/共关I兴 ⫹ k off /k on兲兲 ⫻ 共1 ⫺ exp共⫺共k on关I兴 ⫹ k off兲t兲兲

[A7]

with t ⫽ 0 at the injection start, and for the dissociation phase

APPENDIX 1

B diss共t兲 ⫽ B ass共t 0,diss兲exp共⫺k off共t ⫺ t 0,diss兲兲,

Derivation of an Equation for Analyte-Influenced Drift An expression for the baseline drift during an injection was derived based on the assumption of proportionality between relative binding and relative drift (cf. Fig. 1B): S/S 0 ⫽ 1 ⫺ B/B max

[A1]

where t 0,diss is the time for the start of the dissociation phase. Integration of Eq. [A6] gives: R ass共t兲 ⫽ S 0 共t ⫺ 关I兴/共关I兴 ⫹ k off /k on兲 ⫻ 共t ⫺ 共exp共⫺共k on关I兴 ⫹ k off兲t兲/ 共⫺共k on关I兴 ⫹ k off兲兲兲兲兲 ⫹ C1

giving S ⫽ S 0 共1 ⫺ B/B max兲,

[A2]

where the binding dependent drift is expressed as the slope S at a certain binding level B of an inhibitor, relative the slope unaffected by inhibitor S 0 . B max is the saturated binding level. The model for nonlinear regression analysis of sensorgrams with a constant baseline drift as predefined in the evaluation software BIAevaluation was modified. In this model is B, B max , and a constant slope S 0 , already defined (with other designations). The modification needed is to replace the integrated form of the correction for a constant drift (R is the measured response due to drift and C is the integration constant): dR/dt ⫽ S 0 R共t兲 ⫽

冕

[A3]

S 0 dt ⫽ S 0 t ⫹ C

[A4]

R共t兲 ⫽

冕

S 0 共1 ⫺ B共t兲/B max兲dt

[A9]

and R diss共t兲 ⫽ S 0 共t ⫺ 关I兴/共关I兴 ⫹ k off /k on兲 ⫻ 共1 ⫺ exp共⫺共k on关I兴 ⫹ k off兲t 0,diss兲兲 ⫻ exp共⫺k off共t ⫺ t 0,diss兲兲/共⫺k off兲兲 ⫹ C2

[A10]

respectively. Integration constants were added to the expressions to fulfill the starting conditions R ass ⫽ 0 when t ⫽ 0

[A11]

R diss ⫽ R ass when t ⫽ t 0,diss

[A12]

and

giving the expressions: R ass ⫽ S 0 共t ⫺ 关I兴/共关I兴 ⫹ k off /k on兲 ⫻ 共t ⫺ 共共exp共⫺共k on关I兴 ⫹ k off兲t兲 ⫺ 1兲/ 共⫺共k on关I兴 ⫹ k off兲兲兲兲兲

with the equation for a binding-dependent drift: dR共t兲/dt ⫽ S共t兲 ⫽ S 0 共1 ⫺ B共t兲/B max兲

[A8]

[A5]

[A6]

observing that the binding B(t) is a function of time in the kinetic evaluation.

and R diss ⫽ S 0 共共t ⫺ t 0,diss兲 ⫺ 关I兴/共关I兴 ⫹ k off /k on兲 ⫻ 共1 ⫺ exp共⫺共k on关I兴 ⫹ k off兲t 0,diss兲兲 ⫻ 共exp共⫺k off共t ⫺ t 0,diss兲兲 ⫺ 1兲/共⫺k off兲兲 ⫹ S 0 共t 0,diss ⫺ 关I兴/共关I兴 ⫹ k off /k on兲

[A13]

INTERACTION KINETICS FOR HIV-1 PROTEASE INHIBITORS

⫻ 共t 0,diss ⫺ 共exp共⫺共k on关I兴 ⫹ k off兲t 0,diss兲 ⫺ 1兲/ (⫺共k on关I兴 ⫹ k off兲兲兲).

[A14]

The final expressions used to describe and evaluate the sensorgrams are then for the association phase Eq. [A7] ⫹ Eq. [A13] and for the dissociation phase Eq. [A8] ⫹ Eq. [A14]. This set of equations is the integrated version of Model 1. APPENDIX 2

Model 1: Langmuir Binding with Analyte-Influenced Drift S ⫹ AB ⫹ $1 * RI;

217

AB ⫽ $4兩0; S ⫽ S 0 * 共1 ⫺ AB/R max兲兩0. Model 3: Langmuir Binding with Completely Transport-Limited Interactions AB ⫹ $1 * RI; $1 ⫽ 共sign共t ⫺ t On兲 ⫺ sign共t ⫺ t Off兲兲/2; $2 ⫽ k t * 共$1 * Conc ⫺ K D * 共AB/B兲兲; B ⫽ ⫺$2兩R max; AB ⫽ $2兩0.

$1 ⫽ 共sign共t ⫺ t On兲 ⫺ sign共t ⫺ t Off兲兲/2; $2 ⫽ conc;

REFERENCES

$3 ⫽ k a * $2 * $1 * B ⫺ k d * AB;

1. Wlodawer, A., and Vondrasek, J. (1998) Inhibitors of HIV-1 protease: A major success of structure-assisted drug design. Annu. Rev. Biophys. Biomol. Struct. 27, 249 –284. 2. Markgren, P.-O., Ha¨ma¨la¨inen, M., and Danielson, U. H. (1998) Screening of compounds interacting with HIV-1 proteinase using optical biosensor technology. Anal. Biochem. 265, 340 –350. 3. Markgren, P.-O., Ha¨ma¨la¨inen, M., and Danielson, U. H. (2000) Kinetic analysis of the interaction between HIV-1 protease and inhibitors using optical biosensor technology. Anal. Biochem. 279, 71–78. 4. Holzman, T. F., Kohlbrenner, W. E., Weigl, D., Rittenhouse, J., Kempf, D., and Erickson, J. (1991) Inhibitor stabilization of human immunodeficiency virus type-2 proteinase dimer formation. J. Biol. Chem. 266, 19217–19220. 5. Kuzmic, P., Garcia-Echeverria, C., and Rich, D. H. (1993) Stabilization of HIV proteinase dimer by bound substrate. Biochem. Biophys. Res. Commun. 194, 301–305. 6. Karlsson, R., and Fa¨lt, A. (1997) Experimental design for kinetic analysis of protein–protein interactions with surface plasmon resonance biosensors. J. Immunol. Methods 200, 121–133. 7. Maniatis, T., Fritsch, E. F., and Sambrook, J. (1989) Molecular Cloning: A Laboratory Manual. Cold Spring Harbor Laboratory, Cold Spring Harbor, NY. 8. Alterman, M., Bjo¨rsne, M., Muhlman, A., Classon, B., Kvarnstro¨m, I., Danielson, H., Markgren, P.-O., Nillroth, U., Unge, T., Hallberg, A., and Samuelsson, B. (1998) Design and synthesis of new potent C 2-symmetric HIV-1 protease inhibitors. Use of Lmannaric acid as a peptidomimetic scaffold. J. Med. Chem. 41, 3782–3792. 9. Wachtmeister, J., Muhlman, A., Classon, B., Kvarnstro¨m, I., Hallberg, A., and Samuelsson, B. (2000) Impact of the central hydroxyl groups on the activity of symmetrical HIV-1 protease inhibitors derived from L-mannaric acid. Tetrahedron 56, 3219 – 3225. 10. Myszka, D. G. (1999) Improving biosensor analysis. J. Mol. Recognit. 12, 279 –284. 11. Karlsson, R. (1999) Affinity analysis of non-steady-state data obtained under mass transport limited conditions using BIAcore technology. J. Mol. Recognit. 12, 285–292.

B ⫽ ⫺$3兩R max; AB ⫽ $3兩0; S ⫽ S 0 * 共1 ⫺ AB/R max兲兩0. The first line defines the total response obtained as the sum of drift (S), formation of enzyme–inhibitor complex (AB), and refractive index effects during injection (RI). Lines proceeded by $ are subexpressions. In $1 t On is the time when injection starts and t Off is the time when injection stops. The expression is a step function with value 1 between t On and t Off and else 0. B, AB, and S define differential rate equations for calculation of free enzyme (B), enzyme inhibitor complex, and drift. Starting values for numerical integration are entered after the vertical dash. Model 2: Langmuir Binding Limited by Mass Transport Combined with Analyte-Influenced Drift S ⫹ AB ⫹ $1 * RI; $1 ⫽ 共sign共t ⫺ t On兲 ⫺ sign共t ⫺ t Off兲兲/2; $2 ⫽ conc; $3 ⫽ k t * 共$1 * $2 ⫺ A兲; $4 ⫽ k a * A * B ⫺ k d * AB; A ⫽ $3 ⫺ $4兩0; B ⫽ ⫺$4兩R max;

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12. Nillroth, U., Vrang, L., Markgren, P.-O., Hulte´n, J., Hallberg, A., and Danielson, U. H. (1997) Human immunodeficiency virus type 1 proteinase resistance to symmetric cyclic urea inhibitor analogs. Antimicrob. Agents Chemother. 41, 2383– 2388. 13. Rose´, J. R., Salto, R., and Craik, C. S. (1993) Regulation of autoproteolysis of the HIV-1 and HIV-2 proteases with engineered amino acid substitutions. J. Biol. Chem. 268, 11939 – 11945.

14. Myszka, D. G., He, X., Dembo, M., Morton, T. A., and Goldstein, B. (1998) Extending the range of rate constants available from BIACORE: Interpreting mass transport-influenced binding data. Biophys. J. 75, 583–594. 15. Nascimbeni, M., Lamotte, C., Peytavin, G., Farinotti, R., and Clavel, F. (1999) Kinetics of antiviral activity and intracellular pharmacokinetics of human immunodeficiency virus type 1 protease inhibitors in tissue culture. Antimicrob. Agents Chemother. 43, 2629 –2634.