Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions: SPR Applications in Drug Development

Transcription

1 CHAPTER 5 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions: SPR Applications in Drug Development NICO J. DE MOL AND MARCEL J.E. FISCHER Department of Medicinal Chemistry and Chemical Biology, Utrecht Institute for Pharmaceutical Sciences, Faculty of Science, Utrecht University, P.O. Box 80082, 3508 TB Utrecht, The Netherlands 5.1 Introduction Increasing evidence can be found that describing receptor ligand interactions in terms of a lock-and-key model is no longer adequate. Receptors can be regarded as part of a molecular machinery, in which ligand binding forms a trigger to activate or deactivate the machinery. According to this view, it is no longer sufficient to know how the key fits into the lock, but we should also find out the mechanism with which the key opens and closes the lock. In other words, in drug design we would be interested not only in the affinity of the ligand for the receptor, but also in the changes of a biological receptor molecule when it forms a complex with a ligand. Such changes may involve conformational adaptation, changes in solvation (i.e. ordering of water molecules) and changes in molecular flexibility. Kinetics is a rather underdeveloped aspect of ligand receptor interactions. It is readily conceivable that in some cases, such as in dynamic regulation of signal transduction processes, kinetic control prevails rather than affinity control. Rapid onset of formation and an optimum lifetime of the complex can be fine tuned by appropriate association and dissociation kinetics. Explicit references to the biological significance of binding kinetics are rather scarce; some examples are given by Schreiber [1]. Other examples include the serial triggering 123

2 124 Chapter 5 of T-cell receptors [2] and the activation of the epidermal growth factor receptor ErbB-1 [3]. Elucidation of the molecular architecture, using especially X-ray and NMR techniques has been of crucial importance for understanding how a ligand protein or protein protein interaction functions in the molecular machinery. However, for a more complete understanding of the dynamic processes underlying receptor activation, kinetic and thermodynamic studies of ligand receptor interactions are needed. It is increasingly acknowledged that, to fully appreciate relevant molecular properties of potential drug candidates in a drug design process, there is a need for thermodynamic and kinetic studies [4 8]. Traditionally, van t Hoff analysis has been used for thermodynamic studies. More recently, the use of sensitive calorimetric techniques in drug research is emerging [9,10]. Stopped-flow has been the method of choice to study kinetics of molecular interactions. With SPR one now can derive kinetic and thermodynamic parameters from a single set of experiments. SPR allows to follow the mass change on the sensor surface in real time, yielding affinity and kinetic data. Thermodynamic and kinetic parameters can be derived from a series of experiments in a temperature range. The combination of kinetic and thermodynamic information from well-designed SPR experiments is unique and offers an added value compared with separate techniques for kinetic and thermodynamic information: it allows even a full transition state analysis of the binding process from a single data set. In this chapter, we describe examples of thermodynamic and kinetic analysis of biomolecular interactions using SPR-based approaches that we have developed in recent years. These examples apply mainly to peptides, interacting monovalently or bivalently with important signal transduction proteins, containing Src Homology 2 (SH2) and SH3 domains. These signal transduction proteins are attractive targets for drug design. The underlying investigations are aimed at validation of the SPR-based approach, at gaining insight into the mechanism of the binding process and finally at using this insight in ligand design. To be able to exploit SPR fully, a few initial problems had to be solved. Part of these problems originated from the fact that in our investigations cuvettebased SPR instruments were used. As discussed in Chapters 3 and 4, in flowbased SPR instruments (e.g. Biacore), a continuous flow of the sample enhances diffusion of analyte towards the sensor surface. In cuvette-based instruments, the hydrodynamic properties are controlled by constant agitation of the bulk solution in contact with the sensor surface. The cuvette-based design offers the following advantages: (1) open architecture allowing manual interventions during a run and (2) long association times without extensive consumption of often precious biological material. A disadvantage might be that during the binding process the concentration of unbound analyte in the cuvette is not constant. In this chapter, a correction for this effect is described. Another complication associated with the cuvette design is that in the dissociation phase the analyte released is not removed from the bulk solution. This problem has been solved by adding competing ligand to prevent rebinding of released analyte during the dissociation phase.

3 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions When the association rates are high compared with the diffusion in the bulk solution, mass transport limitation (MTL) occurs. 1 Association and dissociation are affected by MTL to the same extent. We describe a simple method to estimate the extent of MTL. As MTL can be easily included in a simple kinetic model, the experimental association curves can be analyzed. Another problem, not related to instrumental design, is that in principle the affinity of the analyte for the immobilized ligand at the sensor surface, as obtained in a direct SPR assay, is not necessarily identical with that in solution. A method is described to obtain thermodynamic binding constants for the interaction in solution, using competition experiments with a concentration range of the ligand of interest. Using this approach, several ligands can be studied using the same sensor surface. We should emphasize that in this chapter the focus is not so much on theory, but rather on application. We would like to give the reader practical tools to obtain reliable kinetic and thermodynamic parameters on the binding processes. In order to achieve this, we need to provide the corresponding conceptual and theoretical background. Following the outlined approach, reliable kinetic and thermodynamic parameters can be obtained, which can greatly increase our knowledge of binding processes. Later in this chapter we show examples of how kinetic and thermodynamic analysis of interactions using SPR can support chemical biology studies in general and rational structure-based drug design in particular Affinity and Kinetics of a Transport-limited Bimolecular 2 Interaction at the Sensor Surface In a standard SPR assay, one of the interacting partners (the ligand) is immobilized on the sensor surface. The other component (the analyte) is added in the solution, in our case in a cuvette. In our experiments, the ligand is usually a peptide provided with a linker, to increase the distance between the binding epitope and the matrix on the sensor surface, avoiding steric hindrance between the bound analyte and the sensor matrix (see Figure 5.1). The linker is also provided with a free NH 2 terminus, for covalent coupling to the sensor surface using EDC/NHS chemistry. 3 This system guarantees a homogeneous surface by uniform coupling of the ligand through the NH 2 group. The analyte is a protein with generally a much higher molecular weight than the ligand. This increases the sensitivity of the assay, as the change in SPR angle is proportional to the amount of bound mass. Hydrogel SPR sensor chips are used, containing carboxymethylated dextran chains on a 50 nm gold surface (Figure 5.1), either from Biacore (Uppsala, Sweden) or Xantec (Mu nster, Germany). Negatively charged ligands, e.g. peptides 1 For a more detailed treatment of mass transport limitation and diffusion, see Chapter 4, Section A bimolecular interaction is a biomolecular interaction of only one analyte (A) which binds with one ligand (B) to form complex (AB). 3 For further details, see Chapter 7.

4 126 Chapter 5 Figure 5.1 Schematic view showing (a) the SPR sensor matrix existing of dextran chains with carboxymethyl groups on a gold surface (50 nm) before coupling, (b) immobilization of the ligand after coupling and (c) binding of analyte to the surface. containing phosphotyrosines (py), are more difficult to immobilize, due to lack of preconcentration at the sensor matrix, caused by electrostatic repulsion between the negatively charged peptide and the negatively charged carboxyl groups on the dextran chains. In such cases 1 mol l 1 NaCl is added to the coupling buffer to diminish electrostatic repulsion [11]. Our SPR instruments (IBIS and Autolab ESPRIT) have two cuvette cells: a sample cell and a reference cell. The two cells are treated in an identical way, the only difference being that only the sample cell contains immobilized ligands. The net SPR signal (the signal in the reference cell subtracted from the signal in the sample cell) is used for further analysis. Subtraction of the reference signal allows correction for bulk effects due to addition of the analyte, for transient temperature effects and for non-specific binding which occurs incidentally. In a series of experiments at different analyte concentrations, the affinity of the analyte for the immobilized ligand can be assayed in several ways. The method preferred by us is non-linear fitting of the SPR signal at equilibrium with a Langmuir binding isotherm. Alternative methods are based on the kinetics of the interaction. These methods for determining the affinity of the analyte will be described in the following sections Affinity Constants Derived from Equilibrium SPR Signals For a simple bimolecular interaction with molecules A and B forming the complex AB, the equilibrium association constant K A and dissociation constant K D are given by eqs. (5.1a) and (5.1b): K A ¼ ½ABŠ ½AŠ½BŠ ; with K A in l mol 1 ð5:1aþ

5 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions K D ¼ ½AŠ½BŠ ½ABŠ ; with K D ¼ 1 in mol l 1 ð5:1bþ K A where the brackets [A], etc., indicate concentration of the molecules. In a welldesigned affinity experiment, several analyte concentrations are used, which should be in a range around the K D value. In SPR experiments, [AB] and [B] are not approached as concentrations in solution, but as amounts at the surface expressed as SPR signal. The amount of complex AB is proportional to the shift in SPR angle [expressed in millidegrees (m1) or so-called response units (RU)]. A conversion factor can be calculated for SPR response to concentrations in the volume of the 100 nm dextran layer at the sensor surface (see, e.g., Box 5.1). The shift in SPR angle is recorded as function of time in a sensorgram. In Figure 5.2, an example of sensorgrams, based on the net SPR signal (R sample cell R reference cell ), at different analyte concentrations is shown. Using the kinetic evaluation software supplied with SPR instruments, the shift in SPR angle at equilibrium (R eq ) is readily determined (see Section ). Frequently, the data are represented in a Scatchard plot (R eq /[analyte] vs. R eq ) as a straight line. However, large errors can occur in Scatchard plots, especially at low concentrations, with small amounts of binding [13], therefore we prefer non-linear regression using the Langmuir binding isotherm [eq. (5.2)], in which [A] is the free analyte concentration and B max is the maximum binding capacity in m1, when all binding sites on the sensor surface are occupied. ½AŠ R eq ¼ B max ð5:2þ ½AŠþK D Examples of plots with fits according to the Langmuir binding isotherm are shown in Figure Figure 5.2 Sensorgrams (net signal) of binding of v-src SH2 protein to immobilized EPQpYEEIPIYL-peptide. Start of dissociation is indicated by the arrow. v-src SH2 concentrations form top to bottom: 500, 333, 208, 125, 83.3 and 62.5 nmol l 1. For further details, see ref. [12].

6 128 Chapter 5 Figure 5.3 SPR signal at equilibrium as function of analyte concentration. The lines are the fits with the Langmuir binding isotherm [eq. (5.2)]. Data without depletion correction, open circles; with depletion correction (see Section ), closed circles. (A) Binding of v-src SH2 domain (conditions as in Figure 5.2). (B) Binding of Syk kinase tandem SH2 domain. For further details on this interaction, see ref. [14] Correction for Depletion of Free Analyte Concentration in the Cuvette In a cuvette, the free analyte concentration decreases due to binding to the sensor. This section describes how depletion of analyte can be quantified and corrected for. The change in SPR angle (in m1) due to a binding process is directly related to the amount 4 of bound material per mm 2. Under equilibrium conditions the amount of bound analyte is proportional to R eq (in m1) and the surface of the sensor S (in mm 2 ) in contact with the bulk solution. To relate the amount of bound analyte to a decrease in the free analyte concentration, the molecular weight (MW) of the analyte and the volume of the bulk solution (V bulk, in liters) must be known. The depletion correction can be calculated using eq. (5.3). R eq S 10 9 ½AŠ free ¼½AŠ 0 ð5:3þ 122 MW V bulk Here [A] 0 is the initially added analyte concentration in the bulk and [A] free is the corrected analyte concentration, both in nmol l 1. Two examples of depletion correction are presented in Figure 5.3 in (A) for v-src SH2 with molecular weight Da and in (B) Syk kinase tandem SH2 4 For the IBIS and Autolab ESPRIT instruments used by us, an SPR signal of 122 m1 corresponds to 1 ng mm 2 at 25 1C.

7 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions (Syk tsh2) with MW is Da. With eq. (5.3), using values for S (6 mm 2 ) and V bulk (35 ml, the applied volume), the depletion correction is calculated as nmol l 1 /m1 for v-src SH2 protein and nmol l 1 /m1 for Syk tsh2 protein. It is obvious from Figure 5.3 that for Syk tsh2 the depletion correction has a larger effect: without correction K D is 8.7 nmol l 1 and with correction K D is 5.9 nmol l 1. Although the correction factor for v-src protein is larger due to the lower molecular weight, the depletion correction has only a limited effect in this case: K D goes from 294 nmol l 1 without correction to 252 nmol l 1 with correction. For Syk tsh2 the effect of correction on K D is much larger. Owing to the high affinity, the Syk tsh2 concentration used in the assay is very low (Figure 5.3). Depletion caused by binding to the sensor surface has a large effect at low concentrations. Another factor with direct effect on depletion correction is the binding capacity B max of the sensor surface, as it is directly proportional to R eq [see eq. (5.2)]. To minimize depletion and the need for correction, a low binding capacity is advised. In general, a value of B max of 100 m1 (or 500 RU in Biacore systems) is more than sufficient for reliable assays. 5 In equilibrium affinity assays using, e.g., the Langmuir binding isotherm, the depletion correction can be readily calculated by entering the proper numbers in eq. (5.3) and by using a spreadsheet, the correction can be automatically calculated for every data point. Problems may arise when the sensorgrams are used for kinetic analysis. If the depletion correction is large, the free analyte concentration will substantially diminish during the association phase and second order kinetics might apply [15]. In our experience, as long as the depletion correction is below 10% of the total analyte concentration, firstorder kinetics can be safely used [11]. From eq. (5.3) it can be concluded that if B max is below 100 m1, for medium strong interactions (K D E 100 nmol l 1 ) and analyte molecular weights higher than 10 kda, depletion corrections will be smaller than 10%. In kinetic analysis of high-affinity interactions as in the case of Syk tsh2 (see Section 5.4.1), one should be aware of the occurrence of second-order kinetics. In these systems, reliable kinetic analysis is possible based on first-order association kinetics, on surfaces with low B max (B50 m1) and only at higher concentrations, such that depletion correction remains below B10% Affinity Constants and Rate Constants Derived from Kinetic Analysis In the previous section we focused on equilibrium affinity assays based on R eq. Alternatives are offered by kinetic analysis based on the shape of the sensorgrams, which can be useful when the association rate is slow. Especially in flowbased SPR instruments lengthy association times to reach equilibrium may cause problems due to large analyte consumption. 5 Or even lower, depending on the sensitivity of the instrument.

8 130 Chapter k obs Kinetic Analysis Assuming a simple bimolecular interaction with analyte A interacting with immobilized ligand B, forming the complex AB at the sensor surface, ideally the SPR signal vs. time (R t ) is given by eq. (5.4) [16]. R t ¼ k on½ašb max 1 e ðk on½ašþk off Þt k on ½AŠþk off ð5:4þ Here k on and k off are the association and dissociation rate constants for formation and dissociation of the complex AB, respectively. Note that R t is proportional to the amount of complex AB. A new parameter k obs 6 is defined as k obs ¼ k on [A] + k off. Using software that is generally supplied with SPR instruments, a fit of the curve of R t vs. time yields k obs. When k obs is plotted vs. [A], k on can be obtained from the slope of the curve and k off from the intercept. The affinity can be calculated as K A ¼ k on /k off or K D ¼ k off /k on. In Figure 5.4, examples of k obs analysis are shown, using the data sets of Figure 5.3. The parameters of the k obs analysis for v-src SH2 are included in Table 5.1. Although the plots are linear, as expected from theory, the results deviate from the equilibrium analysis. Now for v-src SH2 a K D value of 11.9 nmol l 1 is found, which is almost two orders higher than obtained from the Langmuir binding isotherm. For Syk tsh2 no affinity could be determined using this analysis because the intercept is slightly below zero. The reason for these deviations is that these interactions are severely affected by mass transport limitation (MTL), as appears in Sections and 5.3. Under such conditions, eq. (5.4), which forms the base for this analysis, no longer holds. Schuck and Minton [17] showed with theoretical data how MTL influences the k obs vs. [A] plot. Further examples of how MTL affects the outcome of k obs analysis can be found in the literature [17,18]. As shown above, a straight k obs plot by no means indicates that reliable kinetic data can be derived. Unfortunately, a number of examples of erroneous interpretations of kinetic data can be found in the literature, especially using k obs -analysis or closely related methods. To avoid this pitfall, one should be absolutely sure that MTL is not involved. A number of simple selfconsistency tests, e.g. comparing data from equilibrium and kinetic analyses, should be performed before interpreting such kinetic analysis [20]. A simple experiment to test whether MTL is involved is to measure the effect of addition of binding ligand during analyte dissociation to prevent rebinding (see Section ). The k obs analysis presented in the previous section has severe shortcomings as the outcome is very sensitive to MTL. In the following, an alternative model is offered which also includes MTL. This approach is based on analysis of sensorgrams and curve fitting according to predefined binding models. 6 In earlier publications regarding kinetic evaluations [16], this parameter is denoted k s.

9 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 131 Figure 5.4 k obs plots for binding of v-src SH2 (closed circles) and Syk tsh2 (open circles) to immobilized ligands. Analysis of datasets presented in Figure 5.3. Table 5.1 Kinetic and affinity parameters for v-src SH2 protein binding to immobilized EPQpYEEIPIYL-peptide (experimental data shown in Figure 5.2), as derived with different approaches (see text). CLAMP global analysis Method parameter Binding isotherm k obs analysis Model 1 Model 2 K D (nmol l 1 ) a 308 a 250 a B max (m1) k on (l mol 1 s 1 ) 9.2 (0.3) k off (s 1 ) 1.1 (0.8) b L m (m s 1 ) c Res Ssq d a Calculated from k off /k on. b Experimental value from dissociation in the presence of peptide to prevent rebinding. c Calculated from k tr with conversion factor (see Box 5.1). d Residual sum of squares [19], indicates quality of the fit Global Kinetic Analysis with a Simple Bimolecular Binding Model The real-time information on the mass changes resulting from the interaction can be used to study various binding models, also including MTL. In this

10 132 Chapter 5 1: Bimolecular model 2: Bimolecular model + transport step A+ B kon koff AB A 0 ktr k tr A A+ B kon koff AB Scheme 5.1 Binding models for a simple bimolecular reaction (1) and a bimolecular reaction including a transport step of analyte from the bulk to the sensor surface (2). section, the emphasis is on the rate constants of a simple, transport-limited bimolecular reaction, more complicated binding models are presented in Section 5.4. In this chapter, the kinetic analysis is treated using basic chemical kinetics concepts applied to experimental SPR data. In Chapter 4, kinetics is treated with concepts based on physical solute absorption to surfaces. 7 In general, differential rate equations for species binding to the sensor surface can be derived from a binding model. Experimental sensorgrams can be fitted to a model and one can analyze how far the experimental data agree with the model. Furthermore, parameters such as rate constants and maximum binding capacity can be derived from the fits. In a global analysis such fit procedures are applied to several curves obtained at different analyte concentrations simultaneously, using the same fit parameters. To explain the procedure we use a simple bimolecular binding model with and without mass transport step (see Scheme 5.1). For model 1, the following differential rate equations can be derived: Association : d½abš dt ¼ k on ½AŠ½BŠ k off ½ABŠ ð5:5aþ d½abš Dissociation : ¼ k off ½ABŠ ð5:5bþ dt The analytical solution for the association phase is eq. (5.4) and for dissociation it is eq. (5.6), where [AB] is directly proportional to R t, the net SPR signal at time t, and R eq the net SPR signal at dissociation time zero. Equation (5.6) describes first-order exponential decay from which k off can be obtained. Dissociation : R t ¼ R eq e k off t ð5:6þ Model 2 is somewhat more complicated: again in the association phase the time dependence of [AB] is given by the differential rate equation [eq. (5.5a)], but now also the time dependence of diffusion of analyte from the bulk ([A] 0 )tothe sensor surface ([A]) has to be taken into account. The accompanying rate equations are given in eqs. (5.7a) and (5.7b). d½aš 0 dt ¼ k tr ½AŠ 0 þ k tr ½AŠ ð5:7aþ 7 Remark: this is also the reason why terminology, symbols, etc., differ in Chapters 4 and 5.

11 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 133 Figure 5.5 Global analysis using the program CLAMP of the association phase of binding of v-src SH2 protein to a py-containing peptide (data set as in Figure 5.2). Black lines, experimental curves, red lines, fitted curves. (A) Fit with bimolecular model 1, all fit parameters are left free. (B) Simulation of model 1 with fixed parameters for B max (320 m1), k on ( l mol 1 s 1 ) and k off (2 s 1 ). (C) Fit with transport model 2, with k off fixed on experimental value. See text for further details. d½aš ¼ k tr ½AŠ dt 0 k tr ½AŠ k on ½AŠ½BŠþk off ½ABŠ ð5:7bþ Several programs can be used for solving such differential equations by numerical integration. We used the program CLAMP developed for fitting experimental sensorgrams [19]. 8 Consistency of the fits is greatly improved by fitting several curves for different analyte concentrations simultaneously with the same kinetic parameters in a so-called global analysis. Examples of global kinetic analysis with CLAMP are shown in Figure 5.5, with the data set of Figure 5.2. To emphasize the kinetic phase, only a relatively short association time interval was allowed. The quality of the fits compared with the experimental data is indicated by the residual sum of squares (res Ssq) parameter [19]. For models 1 and 2 this is rather similar (Table 5.1). However, the initial linear phase observed for the higher concentrations is not very well fitted with model 1, and the fit returns a k off value of 0.01 s 1. This linear phase is indicative for MTL [21]. From experiments in the presence of competing peptide to prevent rebinding of protein during the dissociation phase (see Section ), a much higher experimental value of 2 s 1 for k off is obtained. Therefore, we conclude that this model does not yield a satisfactory description of the kinetic parameters. The experimental values of K D and B max are known from the binding isotherm (Figure 5.3), k off is known from dissociation experiments and k on can be calculated from k off /K D. Therefore, all parameters in model 1 are known, allowing simulation of the sensorgrams based on model 1 (Figure 5.5B). This simulation demonstrates that in practice the association phase proceeds much slower than expected for the high on-rate of l mol 1 s 1. This 8 Currently, the features of CLAMP are included in a more extended biosensor data analysis tool named Scrubber2 from the results of David Myszka (see software.html).

12 134 Chapter 5 underscores MTL: due to the high on-rate, diffusion of analyte to the sensor surface is much slower and becomes rate limiting. In model 2, a step for transport of analyte from the bulk to the sensor surface is included. This model, using the fixed experimental k off value of 2 s 1, gives an excellent fit to the experimental data. The diffusion of analyte to and from the sensor surface is assumed to be equal and is characterized by the rate constant k tr. From eq. (5.7b) it follows that the units of k tr obtained from the CLAMP fit are m1 s 1 l mol 1, as [B] and [AB] are in m1 and the fitted curves are SPR signal (m1) vs. time (s). The value of k tr in m1 s 1 lmol 1 can be converted to the mass transport coefficient [21] (L m )inms 1 (see Box 5.1). For v-src SH2 protein (MW ¼ 12.3 kda) this conversion factor is ; applying this conversion yields L m in m s 1. In Table 5.1, the affinity and kinetic parameters derived from global analysis of the dataset of Figure 5.2, using models 1 and 2, are included. The results illustrate once more that in this severely transport-limited system the outcome of k obs analysis is not reliable. The affinity from MTL model 2 agrees perfectly with that from equilibrium analysis using the binding isotherm (Table 5.1). This is not surprising, as in a considerable part of the fitted curves the signal is at equilibrium (see Figure 5.5C). In model 2, the use of an experimental value for k off is crucial for the outcome. In general, it helps to use in the fits fixed experimental values for, e.g., k off and B max. Box 5.1 Conversion of k tr (in m1 s 1 lmol 1 ) into the mass transfer coefficient L m (in m s 1 ) To calculate L m two conversions have to be applied: (1) from m1 to mol m 2 and (2) from l mol 1 to m 3 mol The SPR signal in m1 corresponds to a fixed amount of material/surface unit. For the IBIS and Autolab ESPRIT instruments used in these studies, 122 m1 corresponds to 1 ng mm 2 or 10 3 gm 2. Taking into account the molecular weight (MW) of the analyte, 1 m1 corresponds to MW mol m l mol 1 is 1 dm 3 mol 1 ; this corresponds to 10 3 m 3 mol 1. Combining 1 and 2, the conversion factor from m1 s 1 l mol 1 to m s 1 10 is MW. For v-src SH2 protein with an MW of 12.3 kda, the conversion factor is From the fit with model 2, k tr is found to be m1 s 1 l mol 1. Applying the conversion factor, this corresponds to L m ¼ ms 1. In Biacore instruments, the SPR signal is expressed in response units (RU); 1 RU corresponds to 1 pg mm 2. As 122 m1 corresponds to 1 ng mm 2 (see above), 1000 RU corresponds to 122 m1, and 1 m1 is 8.2 RU. In this chapter, calculations are based on m1. By using the conversion factor of 8.2, these calculations can be adapted for RU-values. It is surprising that the experimental data can be described by such relatively simple models. For example, usually not all binding sites are equal: within the

13 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions dextran layer of the sensor the binding sites more close to the gold surface have a higher intrinsic contribution to the SPR signal, due to the exponentially decaying evanescent field (Chapter 2). Furthermore, especially on high binding capacity surfaces approaching saturation of binding, heterogeneity of binding sites is expected. The global kinetic analysis presented here is attractive because it yields thermodynamic and kinetic parameters. However, one should be careful in the interpretation of kinetic parameters as in the fit procedure these can be mutually correlated [22] and in more complicated binding models the separate steps may not be completely kinetically resolved, as described in Section Detecting Mass Transport Limitation: A Practical Approach Kinetic and affinity analysis with simple models can lead to large errors when MTL is unaccounted for, as shown in Section 5.2. Therefore, it is necessary to detect MTL. In this section, practical methods are described to find transport limitation. 9 Furthermore, we describe here two approaches to obtain true off-rates 10 from severely MTL-affected dissociation phases Effect of Viscosity Change on the Association Phase The essence of MTL is that the on-rate is high and diffusion of analyte from the bulk phase to the biosensor (and partly in the biosensor dextran layer [23]) becomes rate limiting. Viscosity changes of the bulk solution will affect diffusion of the analyte and this should be visible in the sensorgrams of an MTL-controlled interaction. We performed experiments with increasing amounts of glycerol to increase the viscosity. In Figure 5.6, the effect of glycerol on the association of the GST fusion protein of the Lck SH2 domain to immobilized py-peptide is shown. As expected, increasing the viscosity slows down the association. No effect of glycerol in the applied amounts on the affinity was observed (equilibrium signal not affected). Kinetic analysis of data sets obtained with a range of glycerol concentrations, using model 2 (Scheme 5.1), yields a series of k tr values and L m transport coefficients. For flow cells, the flux to the sensor surface due to mass transfer (i.e. L m ) was derived to be proportional to D 2/3 [24]. The diffusion coefficient D is reciprocally related to the viscosity Z, according to the Stokes Einstein equation, and therefore L m should be proportional to Z 2/3. From Figure 5.7, it appears that a plot of L m vs. Z 2/3 yields a linear relation as predicted for flow systems. For a cuvette instrument, the hydrodynamics might be different, as the bulk solution is subject to continuous agitation. Actually, with this data range it is not possible to discern the flow model from other models, as a plot of L m vs. Z also has an excellent linear correlation. 9 For a more basic treatment of mass transport phenomena, see Chapter From theoretical considerations by Schuck and Minton [17], it follows that MTL affects association and dissociation to the same extent.

14 136 Chapter 5 Figure 5.6 Effect of glycerol on the association phase of 30 nmol l 1 Lck SH2 GST fusion protein to immobilized Ahx-EPQpYEEIPIYL-peptide. Solid line, no glycerol; dashed line, 5% glycerol; dot-dashed line, 7.5% glycerol. Reprinted from ref. [11], Copyright (2000), with permission from Elsevier. Figure 5.7 Relation between mass transport coefficient (L m ) from bulk solution to the sensor surface and viscosity (Z) as predicted for the hydrodynamics in a flow cell. Determined in a cuvette based instrument for binding of Lck SH2 GST fusion protein to immobilized EPQpYEEIPIYL-peptide in the presence of 0 to 10% glycerol.

15 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions Attempts to correlate L m values with molecular weight have not been successful. This is probably caused by differences among individual sensors surfaces and the fact that L m depends not only on diffusion in the bulk solution, but also on diffusion within the sensor surface dextran layer as proposed by Schuck [23] Transport Limitation in the Dissociation Phase The high on-rate compared with diffusion also affects the apparent dissociation kinetics. If diffusion is slow and the on-rate is high, a considerable amount of dissociated analyte will rebind before there is an opportunity to diffuse away from the sensor surface into the bulk. This implies that if the association phase is transport limited, the dissociation is also transport limited. In cuvette instruments used in a static mode (i.e. released analyte is not removed from the cell), rebinding will always occur due to the equilibrium between free released analyte in the bulk and bound analyte on the sensor surface, even under conditions that transport limitation does not apply! We present two independent methods to assay true dissociation rates, which gave comparable k off values. The first method takes rebinding into account and the second uses added competing ligands during dissociation to prevent rebinding Rebinding Model for Transport-limited Dissociation If transport limitation applies, the dissociation phase for a simple bimolecular interaction on a homogenous surface will no longer be described by first-order decay kinetics according to eq. (5.6). A high on-rate compared with diffusion away from the biosensor compartment and the availability of free binding sites on the surface will increase rebinding of released analyte. Schuck and Minton [17] have developed a two-compartment model as an approximate description for the dissociation phase under flow conditions. This model is characterized by the differential eq. (5.8). dr t dt ¼ k off R t 1 þ k on k tr ðb max R t Þ ð5:8þ In this model k tr (in m1 s 1 lmol 1 ) has the same meaning as in model 2 (Scheme 5.1) and represents transport between the bulk and the sensor surface. If k tr c k on no transport limitation will occur and eq. (5.8) then changes to eq. (5.5b). (B max R t ) represents the amount of free binding sites and will be proportional to the amount of rebinding. An example of application of this model using the program REBIND 11 is shown in Figure 5.8. Continuous wash steps were performed to remove released analyte. Initially, dissociation proceeds fast (Figure 5.8A), as at the start of the dissociation practically all binding sites are occupied and rebinding is negligible. Soon more binding sites become available, slowing dissociation due to 11 Kindly provided by Dr. Peter Schuck.

16 138 Chapter 5 Figure 5.8 Sensorgrams of binding of Lck SH2 GST fusion protein to immobilized EPQpYEEIPIYL peptide. (A) Solid line, dissociation without renewal of bulk solution; dashed line, dissociation with continuous wash steps to remove released protein from the cuvette. (B) Upper lines: dotted line, experimental data for dissociation with continuous wash steps; continuous line, fit of the data with the program Rebind based on differential eq. (5.8). Below: residuals of the fit. Reprinted from ref. [11], Copyright (2000), with permission from Elsevier. rebinding. Continuous renewal of the bulk solution increases the apparent dissociation rate. The dissociation phase with the wash steps is excellently matched by the model in eq. (5.8) (Figure 5.8B) with B max fixed at the experimental value derived from the binding isotherm [eq. (5.2)]. Using the sum of squared residuals (SSR) analysis of REBIND, a large interval of 0.06 o k off o 0.95 s 1 falls within 5% of the best SSR value (see Figure 5.9, lower curve). In this interval, k off appears to be strongly correlated with k on /k tr. This especially occurs if (k on /k off )(B max R t ) c 1 [see eq. (5.8)], which is the case under conditions of considerable transport limitation (k on and B max R t are large). If a surface is used with a lower B max, effects of transport limitation can be somewhat diminished; however, in a severe transport-limited system, B max should be unrealistically low to prevent transport limitation completely (see Section 5.3.3). Introduction of experimental values for k on and k tr, as derived from global analysis of the association phase with, e.g., model 2 greatly improves the results. As can be seen in Figure 5.9, the SSR analysis indicates a discrete value for k off if k on /k tr is kept at the value from the association phase. The obtained k off -value of 0.38 s 1 is close to the value found for the same interaction (0.6 s 1 ), in the presence of large amounts of competing peptide to avoid rebinding (see Section ). The found value is also in accordance with the rapid dissociation found for other SH2 domains [25]. For several reasons, this result is impressive. First, the slow decay in the dissociation phase in Figure 5.8 in no way suggests such a high k off (see also Figure 5.10). The results confirm that ignoring transport limitation can yield

17 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 139 Figure 5.9 Sum of squared residuals (SSR) as a function of k off. Broken line, analysis with k on /k tr derived from global kinetic analysis of the association phase based on model 2. Reprinted from ref. [11], Copyright (2000), with permission from Elsevier. several orders too low k off values, as can be seen in Table 5.1. Second, the fact that the transport parameter, k tr, derived independently from the association phase, gives consistent results in the dissociation phase is a solid experimental confirmation that both the association phase and the dissociation phase are affected to the same extent by transport limitation, as concluded from theoretical considerations [17]. In practice, it appears that dissociation curves that can be fitted well with eq. (5.8) can also be well fitted by a double exponential dissociation equation for two independent binding sites with each their own dissociation rate [17]. In many cases such a fit will result in an artifact and the obtained rates are not meaningful. Before concluding from a double exponential fit that two different binding sites are involved, a simple consistency check should be performed, e.g. by adding competing peptide to diminish/prevent rebinding (see Section ) Competing Ligand to Prevent Rebinding During Dissociation As indicated in the previous section, under transport-limited conditions the dissociation phase is considerably influenced by rebinding of released analyte. In principle, this rebinding can be prevented by adding an excess of competing ligand with high affinity for the analyte. In Figure 5.10, examples are shown of dissociation in the presence of increasing amounts of competing ligand for a monovalent Lck protein and bivalent binding Syk protein.

18 140 Chapter 5 Figure 5.10 Effect of different concentrations of competing peptide ligand on the dissociation rate. (A) 200 nmol l 1 Lck SH2 GST fusion protein with EPQpYEEIPIYL peptide and (B) 5 nmol l 1 Syk tandem SH2 domain with g-itam peptide. Reprinted from ref. [11], Copyright (2000), with permission from Elsevier (A) and from ref. [14], with permission from Wiley-VCH (B). The effect of the ligands is dramatic and illustrates that for a transport-limited interaction, the off-rate can be several orders larger than expected from the dissociation phase without competing ligand. Although the affinity of these proteins for the ligands is rather high, relatively high concentrations are needed to prevent rebinding completely. In control experiments with high concentrations (4200 mmol l 1 ) of non-binding peptides, the dissociation rate is at maximum, only a bulk effect, a higher baseline is seen, as also occurs in Figure 5.10B, for mol l 1 ITAM peptide. At high concentration of binding peptide the dissociation phase approaches a monophasic exponential decay (see Figure 5.11) and the curve can be fitted with eq. (5.6) to derive the off-rate. In both cases the dissociation rate is very high. For the Lck protein, rebinding (Figure 5.11A) still seems not to be completely suppressed in the presence of even 10 4 mol l 1 peptide. Especially at low R values with more free sites on the surface available for rebinding [see model eq. (5.8)], deviation from first-order decay kinetics is observed; however, the first ca. 80% of the decay can be approximated by the exponential function. The half-lifetime is about 1 s and k off is s 1, close to the value obtained from the rebinding model with fixed experimental value for k on /k tr (0.38 s 1 ; see Section ). The dissociation of the Syk protein (Figure 5.11B) is also speeded up in the presence of competing peptide and shows monophasic exponential decay, with k off ¼ s 1, close to that of comparable mono- and bivalent interactions involving SH2 domains [25,26]. The high dissociation rate in combination with the high affinity (K D ¼ 5 nmol l 1 ) is intriguing. As a rule, high-affinity monovalent interactions have slow dissociation rates, hence the complex has long half-lifetimes, e.g. for the avidin biotin complex it is over 1 week [27]. The binding of a double phosphorylated ITAM-peptide with the tandem SH2

19 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 141 Figure 5.11 Dissociation of bound proteins in the presence of competing ligands to prevent rebinding. (A) Lck SH2 GST fusion protein in the presence of 100 mmol l 1 peptide. (B) Syk tandem SH2 protein with 220 mmol l 1 of bivalent binding ITAM-peptide. The monophasic-exponential or firstorder decay fits [eq. (5.6)] are indicated by the dotted lines. Reprinted from ref. [11], Copyright (2000), with permission from Elsevier (A). domain is bivalent, existing of two weak monovalent interactions (see Section for more structural details). For such multivalent interaction, the dissociation rate approaches that of a single (much weaker) monovalent interaction contributing to the bivalent binding, when competing (monovalent) ligand is present [28]. Therefore, in the presence of proper ligands, multivalent interactions offer the opportunity to combine high affinity with high off-rates and short lifetime of the complex. In signal transduction processes, the combination of high affinity and short half lifetimes might be decisive for specificity and transiency of protein protein interactions. It is remarkable that multivalent interactions, e.g. involving tandem-sh2 and tandem-sh3 domains, are abundant in signal transduction processes Experimental Procedure to Assay High Off-rates Off-rates approaching 1 s 1, as obtained in the previous section, are at the limit of what can be accurately measured by SPR. For really fast decay kinetics we think that the open cuvette structure is an advance as it allows direct accessibility for manual handling. Our protocol developed for assaying rapid dissociation kinetics in cuvette-based instruments starts with setting the instrumental sampling rate high (5 data points s 1 ). The instrument is operated in one-channel mode. A 25 ml volume of the analyte protein, preferably with a concentration that saturates 490% of the binding sites, 12 is pipetted manually into the sample cell. After reaching equilibrium of binding, the measurement is 12 This analyte concentration is approximately 10 K D.

20 142 Chapter 5 started and very quickly 10 ml of a high-concentration competing peptide is pipetted manually. The required concentration of peptide to prevent rebinding has to be determined experimentally (Figure 5.10). The data points of the resulting sensorgram can be exported, processed in a spreadsheet and fitted to an exponential function. The data points within 1 s after peptide addition are discarded, as these are often affected by distortions. The experiment is repeated at least in triplicate with ample manual washing steps in between Quantitative Considerations on Mass Transport Limitation As explained previously, MTL occurs if the reaction (binding) flux is much higher than the transport flux of analyte from the bulk solution to the sensor. These fluxes are described by the transport coefficient L m and the Onsager coefficient L r for the reaction flux [21]. A quantitative measure for MTL is expressed in eq. (5.9). MTL ¼ ð5:9þ L m þ L r If the analyte transport is totally rate limiting in the binding kinetics (L r c L m ), MTL will approach 1. L m is directly related to k tr as defined in model 2 (Scheme 5.1) for the association phase and eq. (5.8) for the dissociation phase. L m in m s 1 is obtained by conversion of k tr as indicated in Box 5.1 in Section The Onsager coefficient of reaction flux (L r )inms 1 is obtained from eq. (5.10) [21]. L r L r ¼ k on ½BŠ ð5:10þ Here k on is converted to m 3 mol 1 s 1 units. 13 At the start of the interaction [B] equals B max, the maximum binding capacity of the sensor surface, i.e. the concentration of free analyte binding sites on the sensor surface. B max can be obtained from the Langmuir binding isotherm [eq. (5.2)] or from global kinetic analysis in m1. Using the same approach as explained in Box 5.1 B max is converted to [B] in mol m 2 with eq. (5.11). ½BŠ ¼ B max MW ðmol m 2 Þ ð5:11þ The extent of MTL allows one to consider whether MTL can be avoided by adaptation of the experimental conditions, e.g. by lowering the binding capacity on the sensor surface or increasing the diffusion rate by increasing flow or agitation of the bulk solution in the cell. The global kinetic analysis with model 2 yields L r ¼ ms 1 and L m ¼ ms 1 for the interaction with v-src SH2 as analyte times k on in l mol 1 s MW ¼ 12.3 kda.

21 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions (see Figure 5.5). Applying eq. (5.9), under these conditions, MTL is practically 1 for this rather high binding capacity surface (B max ¼ 320 m1). To reduce MTL to 0.5 (L r ¼ L m ), the binding capacity B max should be reduced to about 1 m1, which is not a feasible assay condition. Increasing flow and agitation will not be sufficient, either. Assuming that a 5-fold increase in L m can be obtained, the interaction will still be completely transport limited. In practice, the increase in L m will be rather limited due to hydrodynamics (stagnant layer) and the dimensions of the (flow) cells and because diffusion within the dextran matrix on the sensor is not sensitive for the flow conditions [23]. In general, for an analyte protein of approximately 40 kda molecular weight, L m is around ms 1. This number can vary somewhat depending on type of sensor chip. Applying eq. (5.9), this implies that for a surface with B max ¼ 100 m1 (corresponding to mol m 2 ) that L m 4 L r if k on o m 3 mol 1 s 1, corresponding to k on o lmol 1 s 1. This number agrees very well with predictions from various MTL models [17,29]. The size of the analyte, of course, influences the diffusion rate and the k on value, but as a rule of thumb, transport limitation will affect binding kinetics to a dextran-based sensor surface, if k on is larger than 10 5 l mol 1 s 1. In summary, lowering the binding capacity and increasing the flow rate can prevent MTL only in the case of slightly transport-influenced kinetics. In practice, we assume that the L m /L r ratio can be improved at most by about a factor 5 on changing the experimental conditions. As a consequence, in moderately and severely transport-limited cases an effect of MTL on the kinetics cannot be avoided Flow or Cuvette? One can ask whether a flow or cuvette instrument is to be preferred when it comes to transport limitation. Although differences in hydrodynamic behavior may exist between a flow and a cuvette instrument and detailed hydrodynamic models have been derived for flow cells [23,24], in practice, no significant differences in transport fluxes between flow and cuvette systems have been observed. This is illustrated by the agreement of the L m value of ms 1 for IL-2 (MW 14 kda) obtained in a flow-instrument (Biacore) using a model similar to model 2 [30] and the value of L m ¼ ms 1 for the v-src SH2 domain (MW 12.3 kda) obtained in a cuvette instrument (Table 5.1). We conclude that in practice no significant differences exist in the extent of MTL between cuvette and flow instruments. 5.4 Global Kinetic Analysis of Complex Binding Models After describing simple bimolecular interactions, we shift to more complex binding mechanisms with conformational changes, dimerization, multicomponent interactions, multivalent binding, etc. In addition to structural

22 144 Chapter 5 information as derived from NMR and X-ray analysis, kinetic information and insight into the mechanism is valuable for understanding the binding process and is of special interest for rational drug design. We describe examples of applications of global kinetic analysis with more complex models to illustrate this point Global Kinetic Analysis Including Mass Transport and a Conformational Change For better understanding of our first example, the bivalent binding of Syk tandem SH2 domain (Syk tsh2) with a surface loaded with ITAM-peptide, we start with the description of the structural aspects. The interaction of an ITAMderived ligand with Syk tsh2 involves bivalent binding of two phosphotyrosine containing sequences on the ITAM-peptide with the two SH2 domains of the Syk protein. This interaction plays an important role in, amongst others, signal transduction of the IgE receptor (FceRI) and the B-cell antigen receptor [31]. An X-ray structure of Syk tsh2 with an ITAM peptide is shown in Figure The linker part in the ITAM, between the two phosphotyrosine-containing sequences, hardly interacts with the protein [32]. The two SH2 domains in the Figure 5.12 X-ray structure of Syk tandem SH2 domain (ribbon) with doubly tyrosine phosphorylated ITAM (sticks). Both phosphotyrosines are indicated in red. PDB entry 1A81 [32]. Reprinted with adaptation from ref. [14], with permission from Wiley-VCH.

23 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 145 Figure 5.13 Association phase sensorgrams for the interaction of Syk tandem SH2 domain with an immobilized ITAM peptide. Global kinetic analysis of the experimental data using CLAMP, according to the indicated models in red. Reprinted from ref. [14], with permission from Wiley-VCH. Model 3: transport conformation model Model 4: transport dimer model Model 5: 1PP-bivalency model A 0 A+ B AB k k k k A k k AB AB* A k 0 k A A+ B k A+ B AB AB+ B AB2 k AB+ A A2 B k k k k AB Scheme 5.2 Complex binding models used in global kinetic analysis of association phases. Syk protein (labeled N-SH2 and C-SH2) are connected by a flexible coiled coil linker, giving some flexibility in the inter-sh2 distance. The association phase of this interaction was subjected to a global kinetic analysis (Figure 5.13). The association phase was assayed at different temperatures as part of a complete thermodynamic analysis (see Section 5.6 for thermodynamic analysis based on SPR). At 11 1C, deviation is observed using model 2 (Scheme 5.1) in global analysis in the association phase as when the signal approaches equilibrium. It is conceivable that a bivalent interaction occurs in two discrete steps [29], as indicated in Box 5.2. After initial monovalent binding, the second step involves a conformational (intramolecular) change, leading to a high-affinity bivalently bound complex AB* (model 3, Scheme 5.2). This interaction is certainly transport limited, as we see a strong effect of added ligand on rebinding in the dissociation phase (Figure 5.10B). Also indicative of transport limitation is the initially linear association phase, especially at higher analyte concentrations [21]. Therefore, a transport step is included in model 3.

24 146 Chapter 5 Box 5.2 Relation of K b, K conf and K obs in the conformation change model Conformation change model 3 consists of two binding steps (see also Scheme 5.2): an initial binding event occurs, characterized by the equilibrium association constant K b. Second, a structural change in the bound state occurs, characterized by equilibrium constant K conf, leading to a higher affinity complex. For a bivalent interaction as in the case of Syk t SH2 binding to doubly phosphorylated ITAM peptides, this last step includes a structural arrangement of the complex with a second intramolecular binding event. K b and K conf are defined by eqs. (5.12) and (5.13): K b ¼ ½AB1Š ½AŠ½BŠ ð5:12þ K conf ¼ k conf k conf ¼ ½AB2Š ½AB1Š ð5:13þ The observed equilibrium association constant K obs is defined by eq. (5.14): K obs ¼ ½AB1Šþ½AB2Š ½AŠ½BŠ ð5:14þ Note that [AB1] + [AB2] corresponds to the total amount of bound analyte, which is proportional to the change in SPR signal R. Substitution of eqs. (5.12) and (5.13) in eq. (5.14) yields K obs ¼ K b ð1 þ K conf Þ ð5:15þ A plot of R eq vs. [A] will also for this case obey a binding isotherm fit as demonstrated in Figure 5.3, and from the fit B max and K obs are obtained. Applying model 3 gives an excellent fit (Figure 5.13B); in the fits, B max and k off were kept at experimental values. 15 The fit yields the parameters k tr, k on, k conf and k conf ; the values especially of k on, k conf and k conf may not be reliable as they are strongly correlated (see Table 5.2). According to model 3, K obs contains contributions of the initial binding step characterized by association constant K b 15 B max is derived from the Langmuir binding isotherm [eq. (5.2)], which also holds for model 3 (see Box 5.2); k off is derived from the experiment shown in Figure 5.11B.

25 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions Table 5.2 Parameters and their correlation from calculations used in Figure 5.13B. Parameter Value Correlation 1 Correlation 2 Correlation 3 1 k tr (m1 s 1 l mol 1 ) k on (l mol 1 s 1 ) k conf (s 1 ) k conf (s 1 ) and of the second intramolecular binding step or conformation change K conf (see Box 5.2). Notwithstanding uncertainty in the rate constants, a Monte Carlo run 16 with CLAMP gives consistent values for K b (¼ k on /k off ) and K conf (¼ k conf / k conf )of l mol 1 and 18.5, respectively. This value of K b is significantly higher than the l mol 1 found for the monovalent binding of monophosphorylated ITAM peptide [33]. It is likely that the two binding steps in model 3 are not completely resolved. First, no obvious biphasic association phase exists in Figure 5.13; second, by increasing the temperature above 30 1C, we obtain an excellent fit using the bimolecular transport model 2 (Figure 5.13C), indicating that the two binding steps can no longer be discerned. Calculation of K obs from the fit parameters using eq. (5.15) (Box 5.2) yields a value of l mol 1, in excellent agreement with K obs obtained from the binding isotherm at 11 1C ( l mol 1 ). Although the values obtained for K b and K conf may not be physically meaningful, they can be used to calculate solid K obs values with eq. (5.15) Unusual Kinetics: Intermolecular Bivalent Binding to the Sensor Surface A second example from our work where global kinetic analysis plays a central role in elucidating the binding mechanism to a SPR sensor surface is Grb2 protein binding to an immobilized bivalent polyproline (PP) peptide (2PP). 2PP contains two PP binding epitopes derived from the SOS protein 17 separated by a short linker moiety. The Grb2 protein exists of two SH3 domains and one SH2 domain connected by two flexible linkers [34]. The two SH3 domains can each bind to one of the PP epitopes of 2PP in a bivalent mode [34,35]. In Figure 5.14, a model of the bivalent complex of Grb2 protein with 2PP is shown. It was expected that the kinetics of this bivalent interaction could be described by a model similar to that used for the Syk tsh2-itam interaction (Section 5.4.1); instead, a different binding model emerged. The binding of Grb2 to immobilized 2PP SPR sensor surfaces with different binding capacities is shown in Figure The form of the curve describing the association phase 16 In a Monte Carlo run the fit is repeated for a defined number of cycles with variation of the start parameters within a defined range. 17 The SOS-Grb2 interaction plays an important role in the signal transduction cascade of numerous receptors, controlling among others cell proliferation and differentiation, platelet aggregation and T-cell activation [36].

26 148 Chapter 5 Figure 5.14 Model based on X-ray structure of Grb2 (PDB entry: 1GRI, ribbons) which a double polyproline peptide docked on the SH3 domains (sticks). Figure 5.15 Sensorgrams of Grb2 protein (range nmol l 1 ) binding to immobilized 2PP-peptide with various binding capacities (Table 5.3). (A) and (B) net signal (reference cell subtracted from sample cell); (C) data from the sample cell only due to non-specific binding in the reference cell; lowest curve is the baseline not containing Grb2 protein. appears to be sensitive to the binding capacity: at high binding capacities, the association phase looks conventional with a steady increase until equilibrium is reached. Lowering the binding capacity yields biphasic association, with a very fast initial increase, taking only a few seconds, followed by a slower increase (Figure 5.15B and C). The SPR signals at equilibrium apparently comply with the Langmuir binding isotherm [eq. (5.2)], as shown in Figure 5.16 for medium binding capacity. At high and medium capacity surfaces the binding isotherm

27 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 149 Figure 5.16 Equilibrium analysis with binding isotherm of Grb2 protein to a medium high capacity surface of 2PP peptide (data from Figure 5.15B). Table 5.3 Data from binding isotherm of Grb2 binding to 2PP surfaces. Binding capacity B max (m1) K D (nmol l 1 ) High Medium Low 73 3 ND a a ND Not Determined (equilibrium not reached). gave comparable K D values (Table 5.3). At low binding capacities equilibrium is not reached within 20 min (Figure 5.15C). The data from binding of Grb2 to the 2PP surfaces with various binding capacities have been subjected to global kinetic analysis, exploring several models. As shown in Figure 5.17A, the data from very high binding capacity (Figure 5.15A) could be readily fitted with a conformation change model (model 3, Scheme 5.2). Interestingly, the transport step could be omitted from the model, giving identical results. This suggests that in this case the interaction is not transport limited, in agreement with the calculated value of k on ¼ l mol 1 s 1, which is below the indicated value for transport limitation (Section 5.3.3). At medium high and low capacity surfaces, model 3 shows systematic deviations from the experimental data as shown in Figure 5.17B: the slope of the slow phase in the fits changes much less with the concentration than experimentally observed. X-ray structures suggest that Grb2 dimers can be formed [37,38] and therefore the data were fitted with dimer model 4 (Scheme 5.2), as can be seen in

28 150 Figure 5.17 Chapter 5 Global kinetic analysis of Grb2 binding to 2PP surfaces with CLAMP. (A) High binding capacity surface, fitted with conformation change model 3. (B) Medium capacity surface, fitted with conformation change model 3. (C) Medium capacity surface, fitted with dimer model 4. (D) Low binding capacity surface, fitted with dimer model 4. Details of these models are given in Scheme 5.2. Figure 5.17C. The residual sum of squares parameter from the fit with model 4 was 1.71, compared with 2.50 for model 3. Also for the low capacity surface fitting with model 4 gave good results (Figure 5.17D). According to model 4 binding of the first Grb2 molecule (A in the model) to immobilized 2PP (B in the model) facilitates binding of a second Grb2 molecule. However, we doubt that on the surface such physical Grb2 dimer will be formed, because we cannot demonstrate the formation of dimers in solution upon addition of 2PP-peptide to Grb2, either by chemical cross-linking or dynamic light scattering, in line with published results [37]. An alternative to bivalent intramolecular binding is intermolecular bivalent binding (see Scheme 5.3b). In the flexible dextran matrix of the sensor chip, the distance between 2PP epitopes could easily adapt to facilitate intermolecular

29 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 151 Scheme 5.3 Schematic representation of various binding modes of Grb2 protein to 1PP and 2PP surfaces. binding. If intermolecular bivalent binding occurs, this should be observed for a monovalent 1PP surface (Scheme 5.3c). In Figure 5.18, the association kinetics of 1PP surfaces with low and high binding capacity are shown. The curves can be readily approximated with a bivalent binding model: first monovalent binding of Grb2 protein to immobilized 1PP, followed by bivalent binding to a second free 1PP ligand (model 5, Scheme 5.2). As expected, the rate of the slow bivalent binding step depends on the binding capacity: with a high capacity it will be easier to find a second 1PP ligand

30 152 Chapter 5 Figure 5.18 Association phase sensorgrams of Grb2 protein binding to a low (A) and high (B) capacity monovalent 1PP surface. Global kinetic analysis with CLAMP according to bivalent binding model 5 (see Scheme 5.2). and the rate will be higher. Interestingly, the affinity of the initial fast binding step as derived from the kinetic analysis is approximately 12 mmol l 1, which is similar to the affinity of monovalent binding of 1PP to Grb2 in solution [35]. How can the intermolecular bivalent binding mode to the 2PP surface be reconciled with the observed association kinetics which can be well described by the dimer model 4 (Figure 5.17C and D)? We propose a three-step mechanism as outlined in Scheme 5.4: the first step is monovalent (or bivalent) binding of Grb2 to one 2PP ligand; after this, bivalent binding with another 2PP ligand occurs (model 5). This intramolecular binding prepares a perfect second docking site for another Grb2 molecule as the inter-pp distance is already optimal for bivalent binding. This model also explains why the slow phase is much more delayed in case of low binding capacity (Figure 5.17): it is more difficult to find a second partner for divalent binding. The proposed binding model for the 2PP surface cannot be defined in all detail in the CLAMP program, e.g. no bivalent ligands can be defined and no discrimination between single and double occupation of two 2PP ligands can be made. Actually, model 4 is a simplified approximation of the possible binding modes. It is possible that in the dimer complex (step 3, Scheme 5.4) dimeric interactions, as found in the X-ray structure of Grb2 are involved, as the Grb2 molecules are forced to be together. For the monovalent 1PP surface, such dimer formation cannot take place and the kinetics can be adequately described with model Global Kinetic Analysis: Concluding Remarks At first sight, in both examples in this section we have a protein that binds bivalently to an immobilized ligand. However, the outcome is surprisingly different. This is illustrative for the use of models in global kinetic analysis: one

31 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 153 Scheme 5.4 Sequential steps in the proposed model for binding of Grb2 to the 2PP surface, ultimately leading to the formation of dimers. should be very careful in the interpretation of the applied binding model. In complex situations, good fits of the experimental curves can be derived from more than one model. This raises the question of how far the physical reality is reflected by these models. A model will only provide an approximation: not all reactions can be included in detail, as described above. Unless the kinetic steps are well resolved, the calculated kinetic parameters may not be reliable, as they will also be strongly correlated. Hence it is useful to introduce all possible experimental values in the calculations. Other complications may arise from the fact that not all ligands are equally accessible: the sensor with immobilized ligand comprises a three-dimensional

32 154 Chapter 5 volume. Especially for high binding capacity sensors, partition into this volume may be hampered near saturation of binding due to crowding [23]. With multivalent binding analytes the hydrogel of the dextran on the sensor may become more cross-linked, leading to a more compact structure during the binding process. As the SPR signal decreases exponentially with distance from the gold surface (Chapter 2), this might lead to an accounted signal increase vs. the model. In spite of all these considerations, sometimes the quality of the fits with complicated binding models can be stunning (Figures 5.17 and 5.18). As a rule, a proposed binding model should be simple and supported by experimental evidence; additionally, it should include all possible fixed experimental parameters. Global kinetic analysis is a unique tool, providing insight into the binding mechanism, the kinetics of an interaction and the role of protein dynamics. It can inspire new ideas for molecular design and drug development, for example, the length and rigidity of the linker between the two phosphotyrosinecontaining binding epitopes in ITAM-mimetic constructs binding to Syk tsh2 [14]. Ample examples exist using the simple bimolecular models 1 or 2; applications of more complicated models are rather scarce. Such examples are the binding of IL-2 to the heterodimeric IL-2 receptor [30], binding to a heterogeneous surface with two different ligands [39] and the kinetic analysis of amyloid fibril elongation [40]. Deviation from the simple 1:1 model is already indicative of a more complex binding mechanism. 5.5 Affinity in Solution Versus Affinity at the Surface In SPR measurements, interactions take place at the sensor surface, which is not always representative of interactions in solution. This is certainly true for divalent analytes, such as antibodies and GST fusion proteins that form dimers and show an avidity effect when binding to a surface [41]. The amount of analyte binding to the sensor surface in the presence of a competing ligand in solution is influenced by the affinity of the analyte for this ligand. If the affinity is high, a relatively large amount of analyte will be in complex with the ligand in solution and only a small amount of analyte will be available for binding to the surface, resulting in a lower shift in SPR angle. Using this model, Morelock et al. developed a method to obtain thermodynamic binding constants in solution [42]. Based on this, we derived a fitting model for data from competition experiments with constant analyte and varying ligand concentrations in solution (Box 5.3) [43]. An example of competition experiments is shown in Figure Experiments were performed at various ph values to determine the shift in pk a of the phosphotyrosine upon binding [43]. The equilibrium dissociation constant at the chip (K C ) was determined at each ph and these values were used in the fits. The experimental data was fitted with eq. (5.19) (Box 5.3), using experimental values for [A] tot and K C, while the independent variable in the fit is the ligand concentration [B] tot.

33 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 155 Box 5.3 Thermodynamic binding constants for binding in solution In an SPR competition experiment with ligands for the analyte present both on the sensor surface and in solution, the two binding equilibria are as follows: 1. Interaction between analyte A and immobilized ligand B on the sensor chip (Bc), yielding complex ABc on the sensor. The dissociation constant (K C )is K C ¼ ½AŠ½BcŠ ½ABcŠ ð5:16þ [Bc] and [ABc] are in millidegrees; when all Bc sites are occupied [ABc] ¼ B max. 2. Interaction in solution between ligand B in solution with A to form complex AB. The dissociation constant (K S )is K S ¼ ½AŠ½BŠ ð5:17þ ½ABŠ Note that K S is a thermodynamic binding constant. In analogy with eq. (5.2), the amount of binding onto the surface can be described by a binding isotherm: ½ZŠ R eq ¼ B max ð5:18þ K C þ ½ZŠ where [Z] is the total concentration of analyte [A] tot minus the amount of analyte in the complex AB ([Z] ¼ [A] tot [AB]), and eq. (5.18) changes to! ½AŠ R eq ¼ tot ½ABŠ B max ð5:19þ K C þ ½AŠ tot ½ABŠ The amount of complex AB in solution is a function of the affinity in solution (K S ) and eq. (5.17) can be rewritten: K S ¼ ½AŠ tot ½ABŠ ½BŠtot ½ABŠ ð5:20þ ½ABŠ From this equation, it appears that [AB] is a quadratic function of the type ax 2 + bx + c ¼ 0, for which the solution is given by the square root equation ½ABŠ ¼ K q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2þ4½AŠtot S þ½aš tot þ½bš tot K S þ½aš tot þ½bš tot ½BŠ tot ð5:21þ 2 Substituting eq. (5.21) for [AB] into eq. (5.19) yields an equation that fits data from competition experiments. Fitting with [A] tot kept at the experimental value and [B] tot as independent variable provides K S and B max. Note that eq. (5.19) contains K C. The value of K C is obtained from a separate experiment. Best fit is expected when [A] tot Z K C. B max is the maximum binding capacity upon complete saturation, and not the binding capacity in the absence of competing ligand.

34 156 Chapter 5 Figure 5.19 Data from SPR competition experiments to determine the binding constant K S in solution. The analyte is Lck-SH2 GST fusion protein (50 nmol l 1 ), the immobilized ligand and the ligand in solution are identical [a phosphotyrosine 11-mer peptide derived from the hamster middle-t-antigen (hmt)]. Experiments were at different ph: from left to right ph 9, 6.8 and 5. The lines are the fits with the substituted eq. (5.19) (see Box 5.3). Reprinted from ref. [43], Copyright (2002), with permission from Elsevier. In order to verify the reliability of our approach for obtaining affinity data in solution and to see if affinity at the sensor surface is significantly different from that in solution, K C and K S values are compared in Table 5.4. The data illustrate that the affinity of dimer proteins (the GST fusion protein and not-heated Grb2-SH2; see below) at the surface is larger than in solution. This can be explained by the avidity effect, occurring when the dimer binds bivalently to two ligands at the surface. The case of the Grb2-SH2 protein without GST part is interesting. It has been reported that this protein occurs as a dimer. 18 Probably this is an artifact due to the expression as a GST fusion protein, which is known to form dimers through the GST part [44]. From size-exclusion chromatography we estimate that our GST-cleaved Grb2-SH2 protein contains B60% dimer. The dimer is metastable and upon heating to 50 1C the monomer is irreversibly formed [38]. Before heating, the affinity to the sensor surface is higher, due to the large amount of dimer. K S is higher before heating, suggesting that the affinity of the ligand for the dimer in solution is lower than for the monomer. For the pyvnv-peptide binding to monomer Grb2-SH2, consistent values for K S are obtained ( nmol l 1 ), notwithstanding large differences in K C (7.9 for the GST fusion protein to 790 for full-length Grb2) used in the 18 Dimer formation by domain swapping of an a-helix [38].

35 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions Table 5.4 Comparison of affinity at the sensor surface (K C ) and in solution (K S ), calculated from competition experiments using the substituted eq. (5.19) (see Box 5.3). Protein+peptide K C (nmol l 1 ) K S (nmol l 1 ) Lck-SH2 GST fusion protein a + hmt-peptide 6 60 Grb2-SH2 GST fusion protein + pyvnv-peptide Grb2-SH2 not heated b + pyvnv-peptide Grb2-SH2 heated + pyvnv-peptide Full length Grb2 protein + pyvnv-peptide Syk tsh2 + g-itam-peptide v-src SH2 + hmt-peptide a If explicitly indicated the dimer forming GST moiety is present. b Heating to 50 1C converts the Grb2-SH2 dimer irreversibly to the monomer (see text). 157 calculations to obtain K S. Moreover, the solution affinities agree with literature values obtained using other techniques. This strengthens our confidence in the competition approach. As a rule, the affinity of monomer proteins in solution is the same as at the sensor surface, even for the bivalent binding Syk tsh2! An exception seems to be the binding of the full-length Grb2 protein to the SH2 domain. 19 In the case of a bivalent binding analyte with two (identical) binding sites such as an antibody, the expression for [AB] will be different from eq. (5.21). Now we have to take into account that not all occupied antibody remains in solution, as monovalently occupied antibodies are able to bind to the sensor surface. When a certain fraction of all binding sites are occupied, a statistically determined distribution exists over double-bound, single-bound and unbound antibodies in solution. Unbound antibodies, and also a single-bound antibody with a ligand from solution, can bind to the sensor surface. We have adapted the expression for [AB] (Box 5.3) to the statistical distribution [45] and it appears that this correction has only a modest effect on the resulting K S value (o10%). In summary, the approach derived in Box 5.3 cannot be used for every binding model. Especially when the Langmuir binding isotherm is not suitable for fitting R eq as a function of analyte concentration, this approach will not be valid. However, for more complicated binding models obeying the Langmuir binding isotherm, such as the two-step model proposed for Syk tsh2 (Box 5.2), reliable K S values can be obtained. In this case K S will be an apparent binding constant, containing the various contributions to K obs (see Box 5.2). The competition experiments as described in this section are very attractive in drug research: the affinity of a range of potential drug candidates can be assayed at the same surface! In general the standard error in K S is larger than in K C. Processes in solution may not always be representative for processes at sensor surfaces or in biological systems. We are convinced that in some cases interaction at a surface might be a better model than interaction in solution, 19 A possible explanation for this difference is discussed in ref. [12].

36 158 Chapter 5 especially with multivalent interactions. For example, the Sos-protein 20 contains multiple (six) polyproline sequences to recognize Grb2 SH3 domains [36]. Several Grb2 molecules might bind bivalently to these sequences in one Sos molecule in different combinations. For this a surface loaded with polyproline ligands might be a better model than 1:1 interactions in solution. 5.6 Thermodynamic van t Hoff Analysis Using SPR Data As described in the Introduction, it is no longer opportune to describe ligand receptor interactions in terms of a rigid lock-and-key concept. Binding of a receptor by a ligand can influence the dynamics, induce allosteric changes of the receptor or, very importantly, have an effect on bound water molecules. All this can be vital for the biological effects in a biomolecular interaction. In this section we will concentrate on SPR-based assay of thermodynamic parameters, to reveal the biomolecular recognition process, to help understand it and to exploit it for improved rational drug design (see Box 5.4) [5,6,8] van t Hoff Thermodynamic Analysis van t Hoff thermodynamic analysis requires the measurement of the affinity at a range of temperatures. As the SPR signal is extremely sensitive to temperature changes, complications may arise when measuring at temperatures deviating from room temperature, as some time may be needed before complete thermal equilibration is reached. An example is shown in Figure 5.20: in the reference cell a temperature effect is observed in addition to a bulk effect. It takes about 100 s to reach thermal equilibrium. The temperature effect is not visible in the net signal (Figure 5.20). The best approach is to use R eq for the affinity assay as by the time R eq is reached the system will be in thermal equilibrium. It is important, especially when kinetics are assayed, that the sample is at the correct temperature and that the injection system is well thermostated. The design of newer generations of SPR instruments, e.g. Autolab ESPRIT, is optimized for affinity assays in a temperature range C. The simplest case of binding is a bimolecular interaction, such as that between v-src SH2 and hmt-peptide as described above. The van t Hoff thermodynamic analysis of this interaction is shown in Figure The data can be readily fitted with eq. (5.26) and the resulting thermodynamic parameters are included in Table 5.5. The data show that the affinity at the sensor surface (K C ) matches that in solution (K S ), using the method described in Section 5.5. The convex form of the curve indicates a negative value for the heat capacity (DC p ) and this interaction appears to be enthalpy driven. A concise description of how to interpret thermodynamic parameters in terms of molecular events during the binding process is given in Box 5.5. A more detailed interpretation can be found in ref. [12]. 20 This is a crucial interaction in the activation of the Ras signaling pathway described in ref. [36].

37 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 159 Box 5.4 Thermodynamics of binding For the simple bimolecular interaction between A and B yielding the complex AB, the change in Gibbs free energy (DG) is related to the standard Gibbs energy change under standard conditions (1 mol l 1 of A and 1 mol l 1 of B, at 25 1C): DG ¼ DG þ RT ln ½ABŠ ¼ RT lnk a ¼ RT lnk d ð5:22þ ½AŠ½BŠ where R is the gas constant and T is the absolute temperature. DG1 consists of a heat component released or taken up during the binding process (enthalpy, DH1), and an entropy (DS1) component related to the change in the degree of order of the system due to binding: DG ¼ DH TDS ¼ RT ln K a ð5:23þ For protein protein interactions and other biomolecular interactions DH1 and DS1 change with temperature. The temperature dependence of DH1 and DS1 can be described in terms of the heat capacity (DC p ) as given in eqs. (5.24) and (5.25): DH ¼ DH ðt ÞþDC p ðt T Þ ð5:24þ DS ¼ DS ðt ÞþDC p lnðt=t Þ ð5:25þ DC p is assumed constant within the applied temperature range. T1 is the reference temperature, usually 25 1C, and DH1(T1) and DS1(T1) are the values of DH1 and DS1 at this temperature. From eqs. (5.23) (5.25) follows the integrated van t Hoff equation, eq. (5.26), which describes the temperature dependence of the affinity constant K A : ln K A ¼ DH ðt Þ RT þ DS ðt Þ þ DC p R R T T ln T T T ð5:26þ This expression can be used to fit K A values derived at various temperatures versus 1/T, and yields the thermodynamic parameters DH1, DS1 and DC p. A concise description of the interpretation of these parameters in terms of molecular events related to the binding process is given in Box 5.5. Box 5.5 How to interpret thermodynamic binding parameters? It is important to realize that in a thermodynamic analysis two situations are compared: the situation after the process (e.g. binding) is completed, vs. the situation before the process. This is why we look at the difference in the thermodynamic parameters (indicated as D) including the whole of the process, e.g. also the solvent. The thermodynamic analysis of a single interaction usually tells us whether the binding is entropy or enthalpy driven, but it is not possible to interpret molecular processes more in detail, e.g. whether replacement of water molecules is involved or whether protein dynamics decreases. The power of thermodynamic analysis for drug design lies in the combination of 3D structural information and the study of

38 160 Chapter 5 structurally related compounds. This can give detailed insight on how specific structural features contribute to binding energetics. The most important thermodynamic parameters in molecular structural events are: DH binding enthalpy represents the heat effects involved in the interaction. It can be directly experimentally determined with calorimetric measurements. The heat effects are caused by the formation and disruption of non-covalent bonds (hydrogen and ionic bonds and van der Waals interactions) and can involve bonds between the reactants, but also bonds of solvent reorganization and conformational rearrangements of the reactants during the binding process. A large part of DH is due to bulk hydration. In drug design, more water molecules at the interaction interface may extend the complementarity of the surfaces and H-bond networks [9]. This is favorable for enthalpy, but disadvantageous due to a loss in entropy, and contributes to the phenomenon of entropy enthalpy compensation (see text). DS binding entropy can in general be interpreted in terms of degree of order and disorder of the system. This might comprise designed restriction of conformational freedom and rotation of chemical bonds involved in binding. Also, hydration can be a major factor for entropy, e.g. in hydrophobic binding: the burial of water-accessible surfaces and resulting release of water molecules can contribute to binding due to increases in entropy. DC p heat capacity is almost entirely ascribed to solvent effects and is considered of high information content. DC p can be determined directly in calorimetric experiments over a temperature range. DC p can be interpreted in terms of solvent-accessible hydrophobic and polar surface areas, buried in the binding process [5]. A decrease in accessible hydrophobic surface upon binding has a negative effect on DC p ; that of polar surface a positive effect. Experimental DC p values have been related to different degrees of success to 3D structural information on these surface changes upon binding. Problems arise due to solvation effects and release or ordering of water molecules during binding. Ordering of water molecules in the binding interface has a large negative contribution to DC p [4]. Figure 5.20 Temperature effect on SPR sensorgrams. Left: signals of sample cell (solid line) and reference cell (broken line). Right: net signal (reference cell minus sample cell). Reprinted from ref. [46], Copyright (2003), with permission from Elsevier.

39 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 161 Figure 5.21 Table 5.5 van t Hoff plot for binding of hmt-peptide with v-src SH2 domain. (J) Affinity at the sensor surface, K C ;(K) in solution, K S. The lines are calculated using eq. (5.26). Reprinted with permission from ref. [12], Copyright (2005) American Chemical Society. Thermodynamic parameters derived from van t Hoff thermodynamic analysis shown in Figure Parameter v-src SH2 with 11-mer hmt-peptide DH1 (kcal mol 1 ) a TDS1 (kcal mol 1 ) a DC p (cal mol 1 K 1 ) DG1 (kcal mol 1 ) a 9.1 K D (nmol l 1 ) a At reference temperature 25 1C Comparison of SPR Thermodynamics with Calorimetry The heat effects of an interaction can be directly measured using calorimetry. Especially the introduction of isothermal titration microcalorimetry (ITC) instruments with improved sensitivity has greatly advanced the use of calorimetry in biomolecular interactions [9]. A debate is ongoing on the equivalence of enthalpy values from van t Hoff analysis (DH1 vh ), compared to those from calorimetry (DH1 cal ): discrepancies between DH1 vh, from several techniques for affinity assay and DH1 cal have frequently been observed [47 50]. In calorimetric assays the total of the heat effects is assayed, e.g. heat of dilution, of mixing and heat effects due to changes in buffer protonation and solvent equilibria linked with the binding process [47], which go beyond the intrinsic enthalpy contribution of the simple equilibrium A + B " AB. On the other hand, linked equilibria like that of buffers and solvent will also influence the affinity and

40 162 Chapter 5 DH1 vh. The situation may even become more complicated when DC p is not constant with temperature which can occur in multi-step binding processes. Horn et al. demonstrated that, when experimental setup and analysis are performed correctly, there is no statistically significant difference between DH1 values [51]. This holds even for complicated binding models including a conformational equilibrium as shown in Box 5.2. It should be remarked that van t Hoff analysis is peculiar in its error estimation. Recently, Tellinghuisen demonstrated that the usual way of error estimation in van t Hoff analysis is actually not correct and that the errors in DG1, DH1, DS1 and DC p are a function of temperature, leading to relatively large errors in DC p [52]. The number of thermodynamic studies using SPR is rather limited [12,14,50,53 55]. In our experience, the thermodynamic parameters from SPR van t Hoff analysis often compare fairly well with those from ITC [12,14]. As an example, in Figure 5.22 we show the match between our SPR data and ITC data from various studies in an entropy enthalpy compensation (EEC) plot for a wide range of ligands for the Lck and v-src SH2 domains [46]. EEC is a universal phenomenon in biomolecular interactions in water and is generally a problem for the medicinal chemist as a gain in enthalpy, e.g. by adding hydrogen bonds to strengthen the binding, will be counteracted by a loss in entropy [56]. Figure 5.22 Entropy enthalpy plot for binding of various ligands to the Src- or Lck-SH2 domains. Open symbols: data derived from various ITC studies. Closed circles: data derived from SPR competition experiments, with peptide and peptoid ligands. Reprinted from ref. [46], Copyright (2003), with permission from Elsevier.

41 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions Combining SPR and calorimetry to explore fully the thermodynamics and kinetics of interacting systems might provide an optimal approach. To explore the information content of especially DC p values fully, ITC is generally a better choice than SPR thermodynamic analysis. A disadvantage of ITC is that it requires much more material (at least 100 times as much as is needed for SPR). The strong point of the SPR technique is the affinity data and kinetics derived from the same data set Transition State Analysis Using Eyring Plots SPR analysis has the unique feature that kinetic and affinity information can be obtained from one experiment. This implies that thermodynamic experiments can be performed by analyzing the temperature dependence of k on and k off. Eyring s transition state theory provides the fundamental conceptual framework for understanding rates of chemical processes [57]. The transition state (AB # ) is the high energy state along the pathway of reactants to product (for a binding process, the unbound species to the complex). A þ B Ð k 1 AB #! k 2 AB ð5:27þ k 1 Based on eq. (5.27), the thermodynamic equilibrium constant for formation of the transition state is defined as K # ¼ [AB # ]/[A][B]. Applying statistical mechanics, we obtain the Eyring equation state that holds for a rate constant k: k ¼ k BT h K# ð5:28þ where k B is Boltzmann s constant ( JK 1 ) and h is Plank s constant ( J s). K # is related to DH # and DS # (the activation enthalpy and entropy, respectively) in the same way as K A is related to DH1 and DS1 [eqs. (5.22), (5.23) and (5.26)]. This implies that for a linear Eyring plot [ln(kh/k B T) vs. 1/T] the data can be fitted with eq. (5.29). kh In ¼ DH# 1 k B T R T þ DS# ð5:29þ R A non-linear Eyring plot can be fitted with eq. (5.26); such fits yield the activation parameters DH #, DC # p and DS #. Transition state analysis using Eyring plots derived from SPR data have been published elsewhere [12,14,53,54]; an example is given in Figure The k off values at various temperatures were determined in the presence of high concentrations of competing ligand to prevent rebinding (Section ). The k on values were derived from k on ¼ k off /K D. It appears that the Eyring plot for k off is linear, indicating that DC # p is zero between the complex and the transition state (vice versa). The plot for k on shows a convex curvature, indicating that DC # p for formation of the transition state from the reactants is not zero. DC # p has the same absolute value as that derived for DC p from the

42 164 Chapter 5 Figure 5.23 Eyring plots for the interaction of v-src SH2 domain with hmt 11-mer phosphopeptide. (a) k on, fitted with eq. (5.26); (b) k off, fitted with equation (5.29). Reprinted with permission from ref. [12], Copyright (2005) American Chemical Society. van t Hoff analysis of K A for the same interaction (Figure 5.21), because going from the complex to the transition state (k off ) DC # p is zero. The Eyring plot for k on (Figure 5.23a) is interesting as it displays non-arrhenius kinetics above 20 1C, i.e. at higher temperature k on decreases. Non-Arrhenius kinetics have been frequently found for protein folding. A general explanation for this phenomenon is that at higher temperatures a wide region of conformational space is visited and the probability of a flexible ligand or part of a protein having the proper conformation for binding or folding, decreases [58]. Such a model makes sense for the binding of a pyeei-peptide to an SH2 domain, as the high-affinity binding can be regarded as a two-pronged plug into a twoholed socket in need of suitable positioning of the py and I residue for binding [59]. If, for instance, binding starts with the py moiety in its binding pocket, at higher temperatures it will be more difficult to have the I residue in the correct position to allow high-affinity binding. A transition state analysis can give additional information, as is also illustrated by the comparison of binding phosphotyrosine ligands to the v-src SH2 domain vs. Grb2 protein. The affinity and DG1 values are comparable, even the activation energies DG # are nearly identical (Figure 5.24). However, transition state analysis reveals large differences in DH # and DS #. Both DH # values are negative, indicating that upon formation of the transition state, heat is released. The high barrier of activation energy is caused by unfavorable activation entropy contribution. For binding to v-src SH2 this contribution is about 4 kcal mol 1 more unfavorable. This means that formation of the transition state of the Src SH2 domain from the reactants involves a higher degree of ordering than that of Grb2 SH2. Upon binding, the dynamics of Grb2 and v-src SH2 domains is decreased to the same extent, leaving the large difference in DS # unexplained [12]. The difference in thermodynamic behavior can probably be

43 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions 165 Figure 5.24 Energy transitions at 25 1C as a function of the binding coordinate for phosphorylated peptide binding to v-src SH2 domain (solid lines) and to Grb2 SH2 domain (dotted lines). Reprinted with permission from ref. [12], Copyright (2005) American Chemical Society. attributed to the role of water molecules, which form a hydrogen bonding network at the binding interface between ligand and v-src SH2 protein [7] upon formation of the transition state, which has an entropy price. On the other hand, the water molecules in the network make a favorable enthalpy contribution to the transition state, explaining the favorable DH #. For binding to Grb2 SH2, such a role of water molecules is not inferred, only direct contact exists between the ligand and the protein. The above described transition state analysis has been criticized, because it is assumed that every activation leads to complex formation [60]. Alternatively, Arrhenius analysis is advocated [60]. In the interpretation of the data, 3D information from X-ray and NMR analysis is essential. However, the 3D structures alone cannot provide information on energetic contributions determining the binding process. Especially in cases where dynamics of ligand and receptor or solvent effects are involved, results of computational chemistry can be expected to be disappointing. The contribution of entropy to the free binding energy can be very large and may influence the affinity by several orders of magnitude. Thermodynamic and kinetic analysis can help to quantify the extent of these contributions and to generate ideas to exploit them in molecular design. 5.7 SPR Applications in Pharma Research: Concluding Remarks and Future Perspectives In this chapter, we have emphasized the role of kinetics and thermodynamics in biomolecular interactions. Notwithstanding the impressive contributions of structural biology and computational chemistry, our understanding and the ability to predict affinities of receptor ligand interactions remain poor. It is

44 166 Chapter 5 increasingly acknowledged that for a more accurate notion, thermodynamic and kinetic studies of biomolecular interactions are needed. Modern calorimetric and SPR techniques are the tools to perform such studies and deserve a place in the toolbox of rational design used by the medicinal chemist and chemical biologist. The high information content of SPR data with kinetic and affinity information is unique and allows full thermodynamic and kinetic characterization of an interaction, including transition state analysis, as shown in Section There are also limitations to the use of van t Hoff analysis: even with affinity data with relatively small standard errors, DC p has a large error. DC p is important as it can give insight into the nature of the surface area buried upon binding and on the role of water molecules in the binding process (Box 5.5). Using ITC, in general DC p can be more accurately determined by measuring DH at a wide range of temperatures. The best of both worlds is to use SPR and ITC for thermodynamic analysis, with special emphasis on careful experimental design and on the limitations of each method. A concern associated with SPR data is that affinity for a ligand immobilized on a sensor surface might not be identical with that for the ligand in solution. In this respect it is relevant to introduce linkers between the binding epitope and the dextran matrix of the sensor chip, as described in this chapter. In many cases no difference appears, especially for monovalent binding. Using the approach for assays of K S with competition experiments as outlined in Box 5.3, we find comparable affinities at the surface and in solution (see Table 5.4 and Figure 5.21). On the other hand, binding to a surface might be a better model for a biological interaction involving multivalency than (monovalent) interactions in solution. Apart from drug receptor studies, SPR is also useful for other aspects of drug research. Studies on binding to serum proteins are relevant for distribution properties of drugs [61]. Many important drug targets are membrane-bound proteins, e.g. G-protein coupled receptors (GPCRs). Technology to follow passive and active absorption to membrane interfaces using SPR is under development, as is drug binding to metabolizing enzymes [62]. SPR biosensor systems with supported monolayers and tethered bilayer membranes are under development, but not standard technology yet [63]. In an approach called ligand fishing, crude tissue extracts and cell homogenates are screened for potential ligands or targets using SPR [62]. In such approaches, identification of bound species is crucial, with mass spectrometry (MS) as the ideal platform. In particular, matrixassisted laser desorption/ionization time-of-flight MS (MALDI-TOFMS) and electrospray ionization MS (ESI-MS) are powerful tools for protein identification. It is therefore not surprising that it has been attempted to integrate SPR and MS for proteome analysis, as reviewed in ref. [64]. SPR serves two main purposes in proteome analysis: (1) to confirm and possibly quantify specific binding and (2) to act as a micro purification support for further analysis. MALDI analysis directly on a chip surface is possible [65]. Problems may arise due to the small amount of captured protein on the chip, the many handling steps of the procedure and the

45 Kinetic and Thermodynamic Analysis of Ligand Receptor Interactions acidity of the matrix material. In another approach, analytes are eluted and collected in a recovery system. In principle then the whole range of MS techniques, including analysis of digested samples, is available for identification. In drug research, high-throughput screening (HTS) plays an essential role in screening large libraries of compounds. Until recently, the use of SPR technology was hampered by the limited number of surfaces on one sensor chip. In view of the high commercial potential, in the slipstream of the development of array technologies, SPR imaging applications are emerging using microarrays on chips. Examples include Biacore s Flexchip microarray device [66] and IBIS Technologies IBIS-iSPR instrument (see Chapter 6) and other SPR imaging techniques [67,68] (Genoptics and K-MAC, respectively). This field is developing rapidly and is extremely promising. We expect an increasing impact of SPR technology on drug research. This will be enhanced by further developments of SPR technology for pharma applications, such as high-throughput screening, further integration of SPR and MS and mimicking membrane environments and protein ensembles on SPR surfaces. 5.8 Questions 1. What causes mass transport limitation (MTL) in the kinetics of SPR experiments? 2. How can MTL be diminished by experimental design? 3. How can one perform kinetic analysis under MTL conditions? 4. How can depletion of the analyte in a cuvette-based system be calculated? 5. What is the strength of SPR as a tool in drug development research? 6. Explain why a high loading of the ligand affects the determination of the affinity constant. Describe at least two ways to solve this and determine from the sensorgram given below the affinity constant of an antibody antigen reaction in nmol l