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1 Department of Microbiology, Carver College of Medicine, University of Iowa, Iowa 52242, USA
2 National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, Maryland 20892, USA
3 Laboratory of Cellular and Molecular Biology, National Institutes of Health, Bethesda, Maryland 20892, USA
4 Laboratory of Cell Biology, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
(RECEIVED September 13, 2006; FINAL REVISION October 16, 2006; ACCEPTED October 16, 2006)
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Abstract |
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Keywords: ITC; multiprotein complexes; cooperativity; signal transduction; adaptor protein; Sos1; LAT; Grb2; protein interactions; reversible associations
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Introduction |
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TOPAbstractIntroductionResultsDiscussionMaterial and methodsReferences |
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By measuring the changes in the heat content of a reacting mixture in a thermally insulated cell arising from changes in the concentrations of reactants during a titration experiment, ITC directly reveals the enthalpy of binding and, from the shape of the titration isotherm, the free energy of binding and the binding constant. From this, the entropy change of binding can be determined, and through ITC analysis at a range of temperatures, changes in the heat capacity can be measured. For protein interactions, the combination of thermodynamic and structural data has significantly enhanced our understanding of macromolecular interactions in solution (Spolar et al. 1989; Spolar and Record 1994; Baker and Murphy 1998; Tochtrop et al. 2002; Ladbury and Williams 2004), allowing predictions of the size and thermodynamic properties of the binding interface, and the characterization of contributions from protein conformational changes and solvation in the extended binding interface (Cooper 1999; Ladbury and Williams 2004).
The present work is concerned with a slightly different aspect of protein interactions, also a traditional subject of study by ITC, which is the thermodynamic cooperativity of binding at multiple sites for both two-component and three-component protein mixtures. Ternary and higher protein complexes are of significant and increasing interest in many biological systems. Cooperativity is a hallmark of their mode of assembly and interaction, as it provides for a mechanism for information transfer, for the potential to modulate the overall reaction pathway, and for the potential of sharpening the response to changes in local protein concentrations.
A system that will serve as a model for multiprotein complex formation in the present article is the interaction of three proteins involved in signal transduction after T-cell receptor (TCR) activation, LAT, Grb2, and Sos1 (Samelson 2002). The adaptor protein Grb2 contains a single SH2 domain that allows it to bind tyrosine phosphorylated receptors and other adaptor proteins (Koretzky 1997). One of the SH2 domain ligands for Grb2 in a T cell is the adaptor protein LAT, which is rapidly phosphorylated at multiple sites after TCR activation (Samelson 2002). Grb2 also contains two SH3 domains, which function to bring various ligands, including Sos1, an activator of the G protein Ras, to the sites of active signaling (Koretzky 1997). We have recently shown by ITC and multisignal sedimentation velocity that Grb2 can bind multivalently to LAT phosphopeptides that contain two or more Grb2 SH2 domain binding sites at the residues pY171, pY191, and pY226 (Houtman et al. 2006). Similarly, we detected multivalent binding of Grb2 SH3 to the proline-rich regions of Sos1 and Cbl (Houtman et al. 2006). In ternary mixtures of Grb2, LAT peptides containing two Grb2 SH2 binding sites, and Sos1 peptides containing two Grb2 SH3 binding sites, we observed the formation of complexes containing each protein (predominantly with 1:2:1 LAT/Grb2/Sos1 molar ratio), but with a size larger than a 1:2:1 quadruple complex, demonstrating the potential for cross-linking of multiple copies of the adaptor proteins LAT and Sos1 by Grb2. By using confocal microscopy and intracellular signaling assays, we also found that Grb2-mediated oligomerization of LAT and Sos1 takes place in vivo, with functional signaling consequences (Houtman et al. 2006). While the focus of the previous work was to establish the oligomerization of the signaling complexes, it also raised questions about the cooperativity of the interactions in the assembly of the ternary multiprotein complexes. In the present article, the latter question about the energetics and the pathway of assembly was studied in more detail. In order to make this problem more tractable, we simplified the system to eliminate the oligomerization of LAT by using an N-terminal Sos1 fragment Sos1NT containing only a single Grb2 binding site. This provides an upper limit to the size of the complexes that can be formed. As a consequence, the results do not reflect energetic contributions from the cross-linking of multiple LAT molecules into signaling particles but provide a more detailed view of the cooperativity in the mutual interactions of primary and secondary ligands attaching to a single LAT molecule. In the present article, we examine such cooperativity in the formation of ternary LAT/Grb2/Sos1NT complexes by global analysis of ITC injection series in different orientations.
With the goal of characterizing multiprotein interactions by ITC, an important consideration in the design and analysis of the titrations is that for two-component systems the binding isotherms are two-parametric surfaces, which a single ITC experiment can explore only along a one-parametric trajectory determined by the concentrations in the cell and the syringe and the injection schedule. Therefore, when studying complex protein interactions, a single titration may not be sufficient to sample the shape of the binding isotherm and may not allow to derive the binding and cooperativity parameters (Arnaud and Bouteiller 2004). This is even more problematic for three-component mixtures where free, binary, and ternary protein complexes coexist and readjust following several mass action laws after each injection. For such situations to be accessible to ITC analysis, it is critical that many titration experiments with different protein mixtures in the cell and syringe are combined to explore the shape of the isotherm of heat content as a function of three protein concentrations. Only in this case can estimates for binding and cooperativity constants be obtained.
In the present study, we describe the extension of the public domain software SEDPHAT to allow the global analysis of multiple ITC titration experiments for the study of multisite and ternary macromolecular interactions. This software is a widely used platform for the global analysis of analytical ultracentrifugation and dynamic light scattering data, as well as general binding isotherms for a variety of biophysical techniques (Vistica et al. 2004; Balbo et al. 2005; Dam and Schuck 2005). As a first test for consistency with existing ITC data analysis tools, we examined the binding of 4-carboxybenzenesulfonamide (CBS) to bovine carbonic anhydrase II (CAII). This 1:1 bimolecular reaction has previously been used as a benchmark in a comparative study of results from many laboratories (Myszka et al. 2003). After establishing the SEDPHAT platform, the design of ITC titration series for the characterization of more complex, multisite interactions are considered theoretically using simulated binding data. This is followed by the application to two experimental ternary systems of interacting LAT, Grb2, and Sos1 peptides: one exhibiting two monovalent interactions and one exhibiting a combination of a mono- and a bivalent reaction, respectively. Finally, the implications of the results for the assembly of LAT/Grb2/Sos1 complexes are briefly outlined, and the general potential and limitations of the global analysis of orthogonal ITC titrations in the study of multiprotein interactions are discussed.
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Results |
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H(PBS, 25°C) = –10.4 ± 2.5 kcal/mol (error estimates from variation of results among all laboratories) (Myszka et al. 2003). In comparison, the values obtained by us from the SEDPHAT analysis were K = (1.22 ± 0.04) x 106/M and H = –10.65 ± 0.04 kcal/mol (errors from Monte-Carlo analysis of the single isotherm), with a fit of root-mean-square deviation (RMSD) of 0.050 kcal/mol (Fig. 1B,C). Using the VP-ITC instrument analysis software for the same data, we obtained parameter values of K = 0.92 x 106/M and H = –10.8 kcal/mol with a RMSD = 0.109 kcal/mol (the equivalent model in SEDPHAT without baseline offset to account for heats of dilution resulted in the estimates K = 1.07 x 106/M and H = –10.9 kcal/mol with a RMSD = 0.096 kcal/mol).
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H = –10.44 kcal/mol, with incompetent fractions of f CAII = 0.01 for the titration of CBS into CAII and f CAII = 0.21 for CAII into CBS. To highlight the orthogonal nature of the titrations, the inset in Figure 2A shows the negative cumulative heat changes from the two experiments, which jointly define a two-dimensional binding isotherm (except for imperfections due to different incompetent fractions).
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H can be made, due to the correlation of parameter f CAII with K and H. As can be expected, a model that does not account for incompetent material can describe the experimental data well (Fig. 2C, solid line) but results in an underestimate of both K and H (estimates of K = 0.33 x 106/M and H = –9.63 kcal/mol). The parameter correlation is eliminated, however, in the global fit with the pair of conventional titrations. The best global fit (K = 1.40 x 106/M and H = –10.50 kcal/mol) is achieved if a small baseline slope of –0.058 kcal/mol in the dissociation titration is permitted (Fig. 2C,D, residuals). This suggests that the sequentially measured heats of binding are overestimated by an amount that decreases with time, which we attribute to carry-over of heat from incomplete dissociation of complexes within the time allotted between the injections (Fig. 2C, insert). Although the present data show that the dissociation experiment can be included in a global model, this type of titration is not further considered, because it appears to have lower information content and poses increased experimental difficulties compared with the association experiments in either configuration. (In principle, a fourth type of titration can be conceived and could be modeled with the existing software platform—the injection of buffer causing dissociation of complex in the cell due to dilution. This is not explored because it would permit observation of only a very limited concentration range.) In all configurations, the ITC data from the CBS-CAII system can be modeled well globally with a 1:1 bimolecular reaction. This may serve as an experimental control, and suggests that this global modeling approach can be used for the analysis of more complex binding schemes. To this end, we studied next how sets of orthogonal titrations may be useful to characterize cooperativity in multisite binding. Initially, this question can be addressed best theoretically using simulated binding data.
As a model system, we considered a molecule A with two equivalent sites for a molecule B. Figure 3 shows the binding isotherms for the total binding of B, as well as the contributions from singly and doubly occupied A. This plot depicts the binding isotherm as a two-dimensional surface as a function of total A and total B. Also shown are trajectories that would be experimentally explored in the ITC cell during a typical titration experiment of titrating B into A (yellow lines) or A into B (red lines). If the concentrations of [AB] and [ABB] were scaled with the respective molar enthalpy for formation of these complexes, their sum (similar to Fig. 3A) would represent the cumulative total heat in the mixture, and the experimentally measured quantity would be proportional to the slope of discrete segments along the trajectories shown (see also Fig. 2A, insert). Clearly, to characterize the binding properties, the two-dimensional isotherm has to be precisely characterized. In contrast to a simple 1:1 reaction, which would exhibit a symmetrical isotherm, for multisite binding the different titrations carry different information. While the titration of B into A (yellow) leads initially to the formation mainly of 1:1 complexes, followed later by conversion of 1:1 into 2:1 complexes, the reverse titration (red) has initially a very high ratio of 1:2 versus 1:1 complexes and is dominated by conversion of 1:2 into 1:1 complexes. As a consequence, dependent on the orientation of the experiment, the initially measured enthalpy change would reflect mostly either the enthalpy of binding for a single or double occupied complex. Therefore, it can be expected that the analysis is most advantageous if the data from both titrations is combined.
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), and normally distributed noise of 0.050 kcal/mol was added to the simulated data. Analyses were compared for the titration of B into A or A into B alone, respectively, as well as for their joint global analysis. First, we examined the potential for discriminating single-site from two-site binding. For example, for the data in the configuration indicated in Figures 3 and 4, with 10-fold negative cooperativity ( = 0.025), a reasonable fit with an impostor single-site model can be achieved separately for the titration of B into A (K A * = 7.1 x 105/M, H * = –10.2 kcal/mol and f B * = 0.09, 
2 = 1.2), as well as for the titration of A into B (K A * = 4.9 x 105/M, H * = –13.9 kcal/mol and f B * = 0.20, 2 = 2.6), but a misfit in the global analysis is more significant (K A * = 5.7 x 105/M, H * = –13.9 kcal/mol and f B * = 0.20, 2 = 7.4). This shows that the constraints imposed by the global analysis make it easier to identify the presence of the second site. Next, assuming the correct two-site model, we computed estimates for the statistical errors of the best-fit parameter values. Figure 4 shows the ratio of the parameter errors of the local (single titration) analysis relative to the global (both titrations) analysis. Clearly, the absolute value of the parameter uncertainty is dominated by the actual binding parameters and the concentration and molar ratio range covered in the titration. In this regard, the present simulation is a simplification to the extent that the same titrations are assumed in the series of Figure 4. However, it is clear that in all situations the global analysis is significantly better than a single titration. For fundamental reasons, we expect this to hold true also for other analysis models, provided that the experimental titrations do not introduce unrecognized systematic errors between the titrations.
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Recently, we have used such a global analysis in characterizing the binding of Grb2 to Sos1, which has two binding sites for Grb2 (Houtman et al. 2006). It was shown that Grb2 binds to the two sites on Sos1 with significantly different affinity, even though it was not possible to determine whether the reduced binding of a second Grb2 molecule was due to intrinsic structural differences in the binding sites, or due to negative cooperativity. The focus of the previous study was the oligomerization of adaptor proteins into functional signaling complexes by virtue of the simultaneously multivalent interactions of Grb2 with both LAT and Sos1. We now focus on the questions of cooperativity in the assembly of the complex raised in the previous study. The interactions from the LAT-Grb2-Sos1 system will serve as a model to examine the potential of global analysis of ITC titrations. In contrast to our previous work (Houtman et al. 2006), for the present study we use a N-terminal fragment of Sos1, Sos1NT, which is monovalent with regard to the binding of Grb2 and will therefore limit the size of the complex formed. This will make the system more tractable for a more detailed analysis of the energetics of the interactions.
Figure 5 shows a set of titrations for the interaction of Grb2 with Sos1NT, resulting in estimates for the affinity K GS = 2.99 x 106/M and the enthalpy H GS = –23.7 kcal/mol (indicating significant unfavorable entropy S = –57 cal/mol K, consistent with the value reported previously) (Houtman et al. 2006). Importantly, Sos1NT does not interact with LAT peptides (Houtman et al. 2006). For singly and doubly phosphorylated LAT peptides used in the present study, the interactions that occur in binary and ternary mixtures are depicted in Figure 6. The shaded areas indicate reaction paths for the formation of triple complexes. (A table summarizing the titration experiments included in the different analyses is provided in the Supplemental Material.)
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3.7:1, but due to the addition of excess LATpY191 and dilution of the Grb2/Sos1NT mixture in the course of the titration, it can be expected to slightly drop to ([GS] + [LpGS])/[S] 3.3:1 (with an increase in free Sos1NT by 13%). Because of the substantial enthalpy contained in the GS complex (and as follows from fundamental principles), it is important to account throughout the titration for the heats involved in the conversion of all species following mass action law (Equation 2). With a global model for the ternary interaction, best-fit parameters are K LG = 3.48 [2.7 – 3.52] x 106/M (with asymmetric error interval), corresponding to G LpG = –8.9 kcal/mol (Fig. 6, "–8.9" in the green-shaded area), H LG = –(3.9 ± 0.13) kcal/mol, cooperativity factor LpGS = 0.54 [0.49 – 1.3] (corresponding to G LpGS = 0.37 [–0.14 – 0.42] kcal/mol, indicated as " = +0.4" in Fig. 6), and H LpGS = –3.9 ± 2.2 kcal/mol, with a good description of the experimental data (Fig. 7A, solid lines). A model without permitting for cooperativity cannot account for the systematic differences in the initial heats of injection for LATpY191 to Grb2 in the presence and absence of Sos1NT (Fig. 7A, dotted lines). Compared with the simplest possible model of a superposition of independent binding interfaces, this result suggests that cooperativity changes the thermodynamics of the triple complex, by exhibiting a stabilizing enthalpy change that approximately compensates for unfavorable entropy changes, leaving a complex that overall is probably only slightly destabilized.
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G GpL = –8.5 kcal/mol (Fig. 6, "–8.5" in blue-shaded area), H GpL = –6.8 [–6.7 – –8.3] kcal/mol, and cooperativity parameters G SGpL = 0.61 [–0.2 – 0.65] kcal/mol (Fig. 6, " = +0.61"), and H SGpL = –13 ± 7 kcal/mol. This model results in a good description of the experimental data (Fig. 7B, solid lines), in contrast to the best-fit model without cooperativity (Figure 7B, dotted lines). The thermodynamic parameters of the LATpY226-Grb2-Sos1NT interaction are qualitatively similar as with LATpY191, although the enthalpic stabilization appears stronger. Unfortunately, with both LATpY191 and LATpY226 the analysis has the drawback of asymmetric error intervals, and the data do not permit a very precise determination of the binding parameters. Nevertheless, qualitatively the presence of cooperativity can be readily discerned in both cases.
Next, we examined how Grb2 interacts with doubly phosphorylated LAT peptide LATpY191pY226, which forms both binary complexes ("GpLp" and "pLpG"), as well as a triple complex ("GpLpG") (reaction path depicted by the gray-shaded area in Fig. 6, and titration data in Fig. 7C). Under the assumption that the thermodynamic binding parameter of one site is not affected by the phosphorylation of the other site, the microscopic binding constants for each single site can be fixed to values predetermined in the experiments with singly phosphorylated LATpY191 and LATpY226, respectively (see below). In the absence of cooperativity, one would expect this model to give a reasonable description of the experimental data. However, as can be discerned from the large measured initial heats of binding, the molar enthalpy of the GpLpG complex exceeds the sum of the molar enthalpies of GpL and LpG complexes, and correspondingly, the best-fit isotherm cannot describe the data well (Fig. 7C, dotted line). In contrast, a model accounting for cooperativity between the two sites pY191 and pY226 results in a good fit with G GpLpG = 0.33 ± 0.3 kcal/mol and H GpLpG = –3.2 ± 0.2 kcal/mol (Figure 7C, solid line). These values indicate an enthalpic stabilization of the GpLpG complex (as compared to the separate GpL and LpG interfaces), compensating for unfavorable entropic changes, leading to an overall slightly destabilized triple complex.
Finally, we studied the reaction of ternary mixtures of LATpY191pY226 with Grb2 and Sos1NT. Due to the bivalency of LATpY191pY226 for Grb2, each of which can be liganded itself with Sos1NT, mixed complexes, termed "SGpLpG," "GpLpGS," and "SGpLpGS," may occur in solution, in addition to binary and triple complexes examined above (as encompassed by the red dotted line in Fig. 6). Figure 8 shows the experimental calorimetric titration data from injections of LATpY191pY226 into an equimolar mixture of Grb2/Sos1NT. Starting from a minimal model, which assumes that the binding parameters for all molecular interfaces are as predetermined above, and applying the predetermined cooperativity parameters for the triple protein complexes, we calculated the theoretical binding isotherm under the assumption that there are no additional cooperative binding energies (i.e., that the formation of SGpLpG from GpLpG proceeds as in the reaction SGpL 
GpL, that GpLpGS GpLpG has the same parameters as LpGS LpG, and similar for the formation of SGpLpGS). As above, this calculation was based on solving all mass action and mass conservation laws (Equation 2) given the known total concentration of LATpY191pY226, Grb2, and Sos1NT at each point in the titration. The resulting fit is shown in the dotted line of Figure 8. It can be visually discerned that the slope of the inflection point of the data, which is governed by the affinity parameters, is qualitatively higher than in the minimal model. Similarly, the total enthalpies measured qualitatively exceed those predicted by the minimal model. In contrast, a good fit of the data is achieved if cooperativity is permitted for formation of the quintuple complex (leading to estimates for G SGpLpGS = –0.97 [–1.00 – –0.92] kcal/mol and H SGpLpGS = 6.5 ± 0.8 kcal/mol), as shown in the solid line of Figure 8. This would indicate entropic stabilization of the largest complex.
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GpLp, and similar for the GpLpGS GpLpG interaction, respectively), for example, with G SGpLpG = G GpLpGS = –0.37 kcal/mol and H SGpLpG = H GpLpGS = 0.91 kcal/mol. An overview of the free energy changes in the formation of the different complexes is depicted in Figure 6.
In the analysis above, the assumption was made that phosphorylation at Y191 does not influence binding to pY226 and vice versa. We next considered the possibility that LATpY191pY226 exhibits structural differences to LATpY191 and LATpY226, such that the assumption of identical microscopic binding constants as the individual sites would not hold. Unfortunately, modeling the data of Figure 7C assuming the presence of two independent sites, in the absence of a reverse titration, lead to highly correlated parameters. Nevertheless, all models that fit the data resulted in total enthalpy content H GpLpG for the triple complex GpLpG larger by about –3 kcal/mol compared with the sum of the predetermined individual interactions GpL and LpG. We then asked the question what effect the particular assumption on the formation of the GpLpG complex would have on the finding that formation of the quadruple and quintuple complexes exhibit cooperativity. To answer this, we performed a global analysis of the data in Figures 7C and 8, and rather than introducing any particular estimated thermodynamic parameters of the GpLpG complex, we floated all parameters for the formation of GpLp, pLpG, and GpLpG complexes. Keeping the parameters for formation of SG, SGpLp, and pLpGS complexes (i.e., those governing the attachment of Sos1NT) at the predetermined values from the experiments with the respective singly phosphorylated LAT, we searched for the best fit for the hypothesis that formation of SGpLpG, GpLpGS, and SGpLpGS complexes were noncooperative. This constraint led to a 6.4-fold increase in the 2 of the fit, indicating that this model described the data relatively poorly. In contrast, excellent fits were achieved, allowing for cooperativity in the quadruple and/or quintuple complexes. An even worse fit was achieved under the additional assumption that there is no cooperativity in the SGpLp and pLpGS complexes (7.5-fold increase of 2), and further that there is additionally no cooperativity in the GpLpG complexes (8.3-fold increase of 2). A fit of similar quality as those shown in Figures 7C and 8 without invoking cooperativity in the quadruple and quintuple complexes is achieved, for example, when permitting cooperativity in the SGpLp and pLpGS triple complexes, at values different from those determined in the experiments with the singly phosphorylated LAT peptides. In summary, this last exercise shows that the assumption that LAT tyrosine phosphorylation does not globally change the structure of LAT, and only locally enables the binding of Grb2, is necessary for the quantitative analysis of cooperativity in the formation of higher-order complexes, but it is not essential for the qualitative conclusion on the existence of cooperativity in the LAT-Grb2-Sos1NT multiprotein complex assembly.
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Discussion |
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We found that global modeling also improves the discrimination of the correct binding model and stoichiometry. Departing from the traditional use of a parameter "n" that describes a combination of the number of sites and concentration errors, in SEDPHAT only integral numbers of sites are allowed, and concentration errors can be accounted for by separate parameters for incompetent fractions of material. Either method to account for concentration errors requires the resulting parameter estimates to be critically inspected, since large deviations from the expected values may indicate experimental difficulties or application of an incorrect model. The separate treatment of incompetent fractions provides greater flexibility to constrain or float this parameter, for example, by setting upper limits for each incompetent fraction using prior knowledge from known properties of the sample preparation, or allowing it to be different for different experiments (see Fig. 2). In this concept, different binding models may be compared and ruled out on the basis of differences in the quality of fit. In view of the goal to study multiprotein interactions, however, it may be essential to characterize the stoichiometry of the possible complexes by other methods. In this regard, for the system studied in our laboratory, sedimentation velocity has shown to be very complementary to ITC (Balbo et al. 2005; Houtman et al. 2006).
As a model system for cooperative interactions, we have used the proteins LAT, Grb2 and Sos1, for which we have previously observed the formation of multiple binary and ternary complexes (Houtman et al. 2006). Although the data obtained in the present study are limited in that not all thermodynamic aspects are well-resolved, they clearly indicate the presence of both negative and positive cooperativity in the assembly of this multiprotein complex. One could speculate that physiologically such behavior could aid in the assembly of the complex, for example, by suppressing the population of smaller intermediates while promoting the formation of the larger products. Generally the ITC data alone cannot provide a detailed microscopic model for the reaction. Additional data are required to answer questions regarding the molecular mechanism of cooperativity, whether it is mediated by direct contacts, conformational changes, or results from concerted conformational changes of the multiprotein complex (Bray and Duke 2004). Further, the present work did not pursue more detailed thermodynamic aspects that are frequently studied by ITC, such as those concerning the heat capacity changes of the complexes and the role of the solvent. A more detailed discussion of the implications of the results presented here on the cooperativity for understanding the interaction of LAT with other adaptor proteins will be provided elsewhere.
Generally, whether or not the global analysis in SEDPHAT will have sufficient precision to reveal the binding parameters of interest can be tested prior to the experiment, using the tool of simulating titrations for a given experimental configuration. The global fitting strategies may also be applied for the analysis of displacement experiments in the study of very high affinity binding (Sigurskjold 2000), or very low affinity binding (Zhang and Zhang 1998) where sufficiently high ligand concentrations cannot be achieved to permit direct titration (Hu and Eftink 1994). In this case, the displacement isotherm can be obtained as a special case of the general ternary interaction with high negative cooperativity of triple complex formation.
Finally, since the SEDPHAT platform has analysis models for data from other biophysical techniques, the ITC data analysis also has the potential to be extended to multimethod analysis. This may prove advantageous, for example, in conjunction with parallel titration experiments by circular dichroism spectroscopy, surface plasmon resonance, NMR, or hydrodynamic approaches. Multimethod approaches have the promise to better define the molecular binding properties (Tochtrop et al. 2002; Xue et al. 2004; Ladbury and Williams 2006) and, as a consequence, to permit more complex systems to be studied, especially those that cannot be separated in simpler subsystems and for which the analysis by each single technique may not yield unambiguous results. Methods that contribute structural information or site-specific signals would be expected to be particularly useful (Tochtrop et al. 2002; Ladbury and Williams 2006). Global multimethods analysis with the SEDPHAT platform will be explored in future work.
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Material and methods |
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competent cells, and the pRSET bacterial expression vector were bought from Invitrogen. Complete Inhibitor Tablets were acquired from Roche, and the DTT was purchased from Fisher. The amino acids used for peptide synthesis were obtained from Novabiochem, and the TAMRA (5-(6)-carboxytetramethylrhodamine) was acquired from Molecular Probes. Stock solutions of Tris, EDTA, NaCl, and PBS were bought from Biofluids/BioSource. HiTrap chelating HP columns and HiLoad 16/60 Superdex 75 column were acquired from GE Healthcare. The C-4 reverse-phase columns were purchased from Vydac. Carbonic anhydrase Isozyme II from bovine erythrocytes (MW = 30 kDa) and CBS (MW = 201.20 Da) were purchased from Sigma-Aldrich and used without further purification.
Protein purification
Full-length human Grb2 was PCR amplified and cloned into the NheI and EcoRI sites of the pET28+ bacterial expression vector. The full-length proline-rich region (amino acids 1117–1319; Sos1 FL PR) and the N-terminal proline-rich region (amino acids 1117–1215; Sos1 NT PR) of mouse Sos1 were PCR amplified and cloned into the NheI and HinDIII sites of the pRSET bacterial expression vector. The purification of Grb2 and the Sos1 proline-rich fragments were described in Houtman et al. (2006). Briefly, Grb2 and Sos1 expressing BL-21 (DE3) cells were lysed by sonication. The supernatant was applied to a Ni2+-loaded HiTrap chelating HP column, and the proteins were eluted with a gradient of imidazole. The proteins were further purified using a 16/60 Superdex 75 column and then dialyzed overnight against 1x PBS with 2.5 mM DTT. The purified proteins were >95% pure, as assessed by PAGE analysis.
Peptide synthesis
Peptides were synthesized by the solid-phase method with Fmoc (9-fluorenylmethoxycarbonyl) chemistry on a model 431A peptide synthesizer (Applied Biosystems). Phosphotyrosine was incorporated as Fmoc-Tyr(PO3H2)-OH. The peptides were cleaved with a 82.5% trifluoroacetic acid (TFA)/5% phenol/5% thioanisole/5% water/2.5% ethandithiol and then purified by reversed-phase high-performance liquid chromatography (RP-HPLC) on a Vydac C-4 column with 0.05% TFA/water/acetonitrile. The purity of the peptides was determined to be >95% by analytical RP-HPLC. The mass of the peptides was confirmed by matrix-assisted laser desorption ionization time-of-flight mass spectrometry (Micromass).
Isothermal titration calorimetry
ITC measurements of the LAT/Grb2/Sos1 system were performed as described in Houtman et al. (2006). Briefly, all titrations were performed using a VP-ITC calorimeter (MicroCal) in 1x PBS (pH 7.4) with 2.5 mM DTT. The concentration of the injected peptides and proteins were measured by A276, and the proteins were degassed before each experiment.
For the experiments with CAII, the protein was dialyzed extensively against PBS buffer at pH 7.4. The filtered dialysate was utilized to dilute the protein stock to experimental concentration (35 µM) and to prepare a CBS solution at a concentration of 700 µM. Protein concentration was determined spectrophotometrically at 280 nm using a molar extinction coefficient (
280) of 50,700 M–1cm–1. The CBS concentration was determined both spectrophotometrically (210 = 5492 M–1cm–1) and gravimetrically. Both solutions were degassed prior to analysis. The titration was started with an initial injection of 2 µL, followed by 24 injections of 8 µL at 25.0°C. The reverse and the dissociation titration were done analogously. For all experiments, the instrument software was used to determine the normalized heats from each injection. For data analysis, a table containing for each injection the ligand and injectant concentrations, injection volumes, and measured net heats was exported into an ASCII file.
Theory and modeling
The tabulated injection volumes, concentrations of reactants, and the measured heats were loaded into the software SEDPHAT. Functions to recognize exported data formats from different manufacturers are available. Unfortunately, the numerical precision of the ligand and injectant concentrations stored in the ASCII file exported from the instrument software of the VP-ITC is frequently not sufficient for quantitative data analysis. Therefore, based on the known total concentrations of reactants initially in the measurement cell, cX,tot (0), and in the syringe, cX Syr as well as the known total cell volume, V0 , and the injection volumes V(s) (with s enumerating the titration steps), total concentrations of all reactants can be calculated for each step in the titration:
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(The values computed according to Equation 1 are slightly different from those tabulated by the instrument software [MicroCal 1998]. The origin of this discrepancy is not entirely clear, and the user has the choice to base the analysis on values from either Equation 1 or the instrument software. Unless otherwise noted, analyses were based on concentrations from Equation 1.) User input when loading the data will define the type of titration, for example, A into B, B into A, C into mixture of AB, etc., where the designation of reactants A, B, and C is determined by the reaction model.
All models have only integral numbers of binding sites, and models with different predetermined numbers of sites can be compared against each other. This differs from some models in the commercial instrument software, where a floating parameter "n" describes the compound effects of multisite binding and a concentration correction factor (MicroCal 1998; Matulis et al. 2000). In SEDPHAT, in order to account for incompetent fractions of material lowering the true concentration of reactants available for complex formation, each reactant can be assigned a parameter for an incompetent fraction, f, which may be determined by nonlinear regression with f adjusting continuously between 0 and an upper limit f max (with f max < 1). f max may be known from assessment of the quality of preparation by other techniques. Further, the incompetent fraction can be specified to be potentially different in each titration experiment analyzed (a local parameter), or common to all titration experiments. This choice may depend on, for example, whether or not the titrations were done with material from the same preparation, or whether or not there could exist a time-dependent degradation of protein. However, it should be noted that for a binary 1:1 interaction, a transformation of active concentrations c A * = c A, c B * = c B in combination with K A * = K A/ and H * = H/ leaves the calorimetric titration isotherm invariant and is therefore indistinguishable from experimental data. For this reason, an incompetent fraction f should not be treated as a floating parameter in the data analysis for both components of a binary interaction.
In general, with the reactant concentrations cX (X may represent A and B for binary reactions, or A, B, and C for ternary reactions), the known total concentrations cX,tot , and with the complexes species cj of stoichiometries 
j,X , the equations for mass conservation and mass action may be written as
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with s denoting the concentration in equilibrium after s titration steps, and the index j enumerating all different complexes. This equation system can be used to determine all cX,free and hence all complex populations at each point in the titration. Dependent on the model, Equation 2 is solved for all cX,free either with analytical solutions (where available), or in combination of partial analytical solutions [reduction of Equation 2 to the form cX,free (cY,free )] and one- or two-dimensional root-finding algorithms. Full or partial analytical solutions, where available, were computed with the symbolic mathematics toolbox of MATLAB (The Mathworks). No further approximations were used.
The total measured heat content during the injection is
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The first term accounts for the heat content in the cell resulting from chemical reaction of injected reactants with those in the cell. The second term accounts for the heat that evolves when preformed complexes exist in the syringe and are diluted into the cell (Heerklotz et al. 1999). (The latter may be a desirable experimental configuration, for example, when studying ternary mixtures, or self-associating injectants.) Small correction factors 
1 and 2 with 
= 1 ± 0.5V(s)/V 0 account for the fact that the volume of the system does not stay constant during an injection (Merabet and Ackers 1995; Terada and Kuwajima 1999; Arnaud and Bouteiller 2004). In their customary form, they approximate the measurable heat content of the new excess volume V to be an average between the heat content before and after the injection, as this volume element is gradually ejected from the sensitive volume.
Equation 3 can be fitted to the experimental data by global least-squares
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where the index t denotes each titration included in the global analysis, wt is an optional weighting term for of each titration (not used in the present article), and bt is an optional baseline term (floated unless noted otherwise). The latter may account, for example, for the heat of expansion of the reactant from the syringe into the cell (heats of expansion from the cell contents are neglected), or imperfect subtraction of separately measured heats of expansion (Turner et al. 1995). In practice, following the tradition for ITC analyses, the heat changes were normalized relative to the added concentration of the injectant. Simplex, Levenberg-Marquardt, and simulated annealing routines (Press et al. 1992) are implemented to find the global minimum value of the free parameters. Error analysis can be performed in SEDPHAT using either the covariance matrix, F-statistics with projections of the error surface (Bevington and Robinson 1992; Johnson and Straume 1994; Turner et al. 1995), or Monte-Carlo simulations.
Dependent on the specific reaction model, the binding constants Kj and enthalpy changes Hj were expressed such that cooperativity effects are apparent. For example, for a reaction of B binding to A at two identical sites, the macroscopic binding constants K' are expressed on the basis of the microscopic binding constant for a single site KAB and a cooperativity factor , and similarly an enthalpic contribution to cooperativity H :
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This parameterization of the binding constants and enthalpy changes can be useful to apply constraints (for example, utilizing values of KAB from prior knowledge, or testing the absence of cooperativity = 1 and H = 0). An alternate binding model of A with two sites for B is available, where the microscopic binding constants for site 1 and site 2 can be specified individually, and cooperativity is expressed as a separate parameter. However, the two binding and the cooperativity constant cannot be determined simultaneously.
For the simplest ternary interaction of A having one site each for B and C, it is c AB = K AB c A c B, c AC = K AC c A c C, and cABC = K AB K AC c A c B c C, which is solved simultaneously with mass conservation laws. Here, microreversibility requires that cooperativity of adding C to a pre-existing AB complex is equal to the cooperativity of adding B to a pre-existing AC complex, and therefore only a single cooperativity parameter for the affinity is necessary, and a single parameter for the enthalpic contributions to cooperativity, H = H ABC – (H AB + H AC). Similarly, higher-order interaction models were implemented: for a molecule A having two sites for B and one for C (which can form quadruple complexes); and for a molecule A having two sites for B with each B, in turn, having one site for C (which can form quadruple and quintuple complexes).
The software SEDPHAT can be obtained from the author (P. Schuck) or be downloaded from http://www.analyticalultracentrifugation.com/sedphat/sedphat.htm, where tutorials and examples for its application can also be found, as well as an e-mail based discussion forum for users. Future extensions of the SEDPHAT global analysis platform for ITC titrations are planned to include models for linked protonation (Baker and Murphy 1997).
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Footnotes |
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Reprint requests to: Dr. Peter Schuck National Institutes of Health, Bldg. 13, Rm. 3N17, 13 South Dr., Bethesda, MD 20892, USA; e-mail: pschuck{at}helix.nih.gov; fax: (301) 480-1242.
Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.062558507.
Abbreviations: ITC, isothermal titration calorimetry; H, enthalpy change of binding; K A, binding association constant; LAT, linker for activation of T cells; Sos1, son of sevenless homolog 1; Grb2, growth factor receptor-bound protein 2; CAII, bovine carbonic anhydrase II; CBS, 4-carboxybenzenesulfonamide.
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References |
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TOPAbstractIntroductionResultsDiscussionMaterial and methodsReferences |
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Arnaud, A. and Bouteiller, L. 2004. Isothermal titration calorimetry of supramolecular polymers. Langmuir 20: 6858–6863.[CrossRef][Medline]
Bains, G. and Freire, E. 1991. Calorimetric determination of cooperative interactions in high affinity binding processes. Anal. Biochem. 192: 203–206.[CrossRef]
for each parameter were determined from a model assuming unknown binding parameters, incompetent fractions, and a constant baseline offset, using Monte-Carlo error analysis. Ratios of errors are plotted for the titration of B into A (open symbols) and B into A (solid symbols), for the log10 of the binding constant (squares), 
