Abstract
Background
Empirical binding models have previously been investigated for the energetics of protein complexation (ΔG models) and for the influence of mutations on complexation (i.e. differences between wildtype and mutant complexes, ΔΔG models). We construct binding models to directly compare these processes, which have generally been studied separately.
Results
Although reasonable fit models were found for both ΔG and ΔΔG cases, they differ substantially. In a dataset curated for the absence of mainchain rearrangement upon binding, nonpolar area burial is a major determinant of ΔG models. However this ΔG model does not fit well to the data for binding differences upon mutation. Burial of nonpolar area is weighted down in fitting of ΔΔG models. These calculations were made with no repacking of sidechains upon complexation, and only minimal packing upon mutation. We investigated the consequences of more extensive packing changes with a modified meanfield packing scheme. Rather than emphasising solvent exposure with relatively extended sidechains, rotamers are selected that exhibit maximal packing with protein. This provides solvent accessible areas for proteins that are much closer to those of experimental structures than the more extended sidechain regime. The new packing scheme increases changes in nonpolar burial for mutants compared to wildtype proteins, but does not substantially improve agreement between ΔG and ΔΔG binding models.
Conclusion
We conclude that solvent accessible area, based on modelled mutant structures, is a poor correlate for ΔΔG upon mutation. A simple volumebased, rather than solvent accessibilitybased, model is constructed for ΔG and ΔΔG systems. This shows a more consistent behaviour. We discuss the efficacy of volume, as opposed to area, approaches to describe the energetic consequences of mutations at interfaces. This knowledge can be used to develop simple computational screens for binding in comparative modelled interfaces.
Background
Macromolecular complexation is key to many biological processes, and has been a subject of experimental study for many decades. The last few years have seen significant advances in high throughput detection of proteinprotein interactions, for example with yeast two hybrid [1] and affinity purification methods feeding into analysis by mass spectrometry [2]. These laboratory advances have led to a new area of bioinformatics analysis, interpreting the data in terms of interaction networks, and putting such networks in a biological context [3]. At the same time, structural biology continues to visualise interfaces at atomic resolution [4,5], whilst computational biology addresses whether proteins can be docked into the correct complexes [6,7], and develops models for the prediction of binding affinities [8]. These are fundamental questions, combining the physicochemical properties of atomic interactions with biological activity.
Docking of two proteins is determined by complementarity of shape and of pairwise interactions within shapematched patches [9]. Methods for predicting mainchain alteration are still relatively poor, so that successful docking methods have been largely restricted to proteins for which there is little conformational change between the complexed and uncomplexed forms [10]. The issue of sidechain rotameric variation upon complexation can also cause problems [11], necessitating the development of methods to sample sidechain conformers [12]. There are promising advances in the handling of conformational variation, for both sidechains and mainchain, which simulate variation and show that the correct solution can be identified in a cluster of wellpacked configurations [13,14].
Computational research in protein docking inevitably overlaps studies that construct models for binding affinities, through the common use of forcefields. One particularly important growth area is the assessment of binding potential for proteins that are homologous with the constituents of characterised complexes i.e. comparative modelling of complexes based on known interfaces [15,16]. Whereas comparative modelling of individual domains based on homology demonstrates the fold for the sequence of interest, albeit with variations that may not be easy to model, similar modelling applied separately to noncovalently linked components must address the question of whether a viable interface is maintained. If effective algorithms can be developed in this area, then structural bioinformatics, combined with structural biology, will be a valuable complement to the high throughput experimental methods for determining proteinprotein interactions. The question of what features determine interfacial stability had been extensively studied. A recurring theme is the importance, in many cases, of buried nonpolar area [17]. This simple observation, along with the complexity and computational scale of attempts to calculate free energies of binding by simulation, has led to the development of empirical binding models [8]. These involve the separation into terms that each represent some physical feature or combination of features, and which are linearly combined and the relevant weights determined through fitting to a test set of experimental data. Terms reflect properties such as: the hydrophobic effect/buried nonpolar surface area; electrostatic interactions; van der Waals interactions; sidechain rotameric entropy; rotational and translation entropy of complexation. The limitations of such models, especially the lack of a simulation component, are counteracted by their potential to detect trends through fitting to experimental data.
There is also widespread interest in modelling the influence of mutations at interfaces, which in biological terms could map for example to the role of single nucleotide polymorphisms in complexes [18]. Binding models have been derived from fitting to measured differences in binding energies for mutant complexes relative to wildtype [19,20]. In the current work, we denote models for binding in complexes as ΔG models, and those for differences (upon mutation) between complexes as ΔΔG models. Since ΔG and ΔΔG models use the same range of terms, apart from cancellation of rotational/translational entropy, it is of interest to compare them. This is the subject of the current study.
An important property of interfaces is the degree to which conformation changes between the complexed and uncomplexed forms. We have restricted our dataset of wildtype proteins to those for which there is no evidence in the literature for mainchain changes, and for mutant proteins the assumption is made that the backbone does not change. With regard to sidechains, we make use of a mean field technique adapted previously in our laboratory [21], from earlier work [22]. With this method the probability of a rotamer is higher where it can fit with a larger number of neighbouring sidechain rotamers, at a given van der Waals tolerance. Thus higher probability values, in this framework, tend to select rotamers with higher solvent accessibility, and conversely lower probability generally maps to lower solvent accessibility. Rotamer prediction is more difficult for sidechains without structural constraints [23], and prediction accuracy reduces in these cases for commonlyused methods such as SCWRL [24]. In the current work we study the effect of differential modelling of interfacial changes, using either the higher solvent accessibility scheme ("HighSA"), or in the lower solvent accessibility ("LowSA") scheme. Comparison with accessible solvent areas in experimental structures suggests that the more compact, LowSA, configurations may give a more appropriate representation.
In addition to the question of how to repack sidechains, there is also the issue of which sidechains to repack. In a minimal scheme for repacking, using the experimental rotamers where possible, wildtype complexes are not repacked at all, and mutations are modelled simply by rotamer selection for the mutated amino acid. Such structural models we denote as "Minimal". In contrast, it is also possible to repack all sidechains for all molecules, so that the packing can (in principle) change upon complexation and/or upon mutation. We label such schemes as "Complete". Thus MinimalHighSA packed wildtype complexes in ΔG models are simply the structures from the experimentallydetermined complexes, and for mutations in ΔΔG models would simply be modelling of the mutated residue with the most solvent accessible rotamer, in the free and complexed states. CompleteLowSA takes low solvent accessibility rotamers, and repacks all sidechains, in both free and uncomplexed states.
Our results show that the importance of buried nonpolar surface for ΔG models is not reflected in ΔΔG models, when using HighSA packing (Minimal or Complete). We examine the effect of CompleteLowSA packing, allowing for greater environmentspecific relaxation. Although the magnitude of calculated nonpolar burial differences between wildtype and mutants is increased, the CompleteLowSA packing does not significantly improve consistency between ΔG and ΔΔG models. A key factor in the inconsistency is that changes in nonpolar burial upon mutation can be either positive or negative, in comparison with the experimental ΔΔG values in our dataset that are almost exclusively unfavourable upon mutation. This is true for all packing schemes used, presumably reflecting inaccuracies in predicting conformation upon mutation and/or that structure is more fluid than can be represented by single conformers.
The inconsistency of ΔG and ΔΔG models is substantially reduced when a simple volumebased representation of interfacial changes replaces the areabased description. We discuss this result in the context of comparative modelling for proteinprotein interfaces.
Results and discussion
Nonpolar surface area dominates ΔG binding models (no sidechain repacking)
A set of proteinprotein complexes with known structures and binding energies was collated as described in the Methods section. We ascertained that there was no evidence for substantial mainchain conformational change in these complexes through a survey of the literature. Although structures for the uncomplexed components were not used in calculations, in several cases these were used for assessment of conformational change. Table 1 lists the set of wildtype complexes used in the current study, together with their complexation energies.
Table 1. Wildtype complexes and binding energies.
Figure 1 shows best fit models for the wildtype complexes, setting ΔG_{ROTTRANS }to zero. Table 2 gives the model weights corresponding to Figure 1, and with models calculated for ΔG_{ROTTRANS }= 10 kJ/mole, investigating the range derived from experiment [25]. There is very little difference in models at 0 or 10 kJ/mole for ΔG_{ROTTRANS}, and this is generally true throughout this work. The Methods section describes modelling of ΔG_{SCROT }according to a Locked scheme (sidechains free in separated components and fixed in the interface), and an Unlocked scheme (free at all points). Comparing Figure 1 panels (a) and (d), and also Table 2, whilst there are some differences between the Locked and Unlocked interfacial sidechain models for ΔG_{SCROT}, with somewhat better performance for the Locked case, the overall domination by ΔG_{ASANP }is common. Figure 1(c) shows that Locked ΔG_{SCROT }values are, as expected, substantially larger than the Unlocked sidechain ΔG_{SCROT }values, but with little correlation between them. Table 2 indicates that the best fit model uses a negative (unphysical) weight for Unlocked interfacial sidechain ΔG_{SCROT}. Generally, several of the weights reported in Table 2 are negative. Where these are of small magnitude they will have little contribution to a binding model, and larger magnitude negative weights are likely to result from anticorrelation with other features that have large and positive weights. Table 3 shows correlations between calculated properties, and between calculated properties and experimental binding energies. The correlation shown in Figure 1(b) and the weights in Table 2 make it clear that buried nonpolar area dominates the ΔG binding model [17].
Figure 1. ΔG models with Locked and Unlocked interfacial sidechains, MinimalHighSA. Binding models are fit to wildtype ΔG_{EXP}, and MinimalHighSA implies no repacking for wildtype systems. (a) Model fit with ΔG_{SCROT }calculated for Locked interfacial sidechains and ΔG_{ROTTRANS }= 0 (R^{2 }= 0.69). (b) Correlation between ΔG_{EXP }and Δ(ASANP) (R^{2 }= 0.55). (c) Poor correlation (R^{2 }= 0.12) between ΔG_{SCROT }calculated with Locked and Unlocked interfacial sidechains. (d) Model fit with ΔG_{SCROT }calculated for Locked interfacial sidechains and ΔG_{ROTTRANS }= 0 (R^{2 }= 0.61). For plots with equivalent y and x quantities, the line y = x is shown.
Table 2. Weights for ASAbased binding models.
Table 3. Correlations (R) for ΔG model features in wildtype complexes, MinimalHighSA packing
Nonpolar surface is a minor feature in ΔΔG binding models (minimal sidechain repacking, MinimalHighSA)
Empirical binding models generally target either complexes or differences between wildtype and mutant complexes, but not both. We are interested in whether ΔG and ΔΔG models show the same relative importance of model features. Figure 2 shows results for ΔΔG models, where the rotation/translation term cancels between wildtype and mutant systems. Again reasonable fits are obtained, although this time the Unlocked interfacial sidechain entropy term gives a slightly better model than the locked term (compare panels (a) and (b) of Figure 2). As for the wildtype calculations, these two terms do not correlate well (not shown). A major difference to ΔG models (Table 2) is that nonpolar surface area has a small weight, and a poor correlation with the measured binding data (Table 4). The ΔΔG_{ASAP}, ΔΔG_{IONISDESOLV }and ΔΔG_{SCROT }terms correlate to such a degree that individually they can adopt a large and unphysical weighting, with compensation by the other features.
Figure 2. ΔΔG models for Locked and Unlocked interfacial sidechains, MinimalHighSA. Binding models fit to ΔΔG_{EXP}, for MinimalHighSA repacking. (a) ΔG_{SCROT }calculated for Locked interfacial sidechains (R^{2 }= 0.61). (b) ΔG_{SCROT }calculated for Unlocked sidechains (R^{2 }= 0.64).
Table 4. Correlations (R) for ΔΔG model features (mutant and wildtype complexes differenced), MinimalHighSA packing
A ΔG binding model fits poorly to measured ΔΔG (minimal sidechain repacking, MinimalHighSA)
Figure 3 demonstrates discrepancy between ΔG and ΔΔG models. The ΔG model of Figure 1(a) (see also Table 2) has been applied to the mutant complexes, and compared with measured ΔG. Within clusters (representing the mutant sets), the spreads of calculated ΔG are too small to reproduce variation in the measurements. This issue of model incompatibility is not resolved when a single ΔG model is fit to ΔG data for wildtype and mutant complexes (not shown). Some resolution of the discrepancy could be achieved if assessment of buried nonpolar area were inaccurate in ΔG or ΔΔG models, and/or if the strategies for mutant selection, and perhaps the systems undergoing mutagenesis, emphasise other features over nonpolar properties. The second factor is unlikely to be the whole story, since polar features are downweighted in the ΔG models. With regard to the first factor, the meanfield packing algorithm has been modified such that sidechain rotamers can be chosen that will tend towards maximal packing with the rest of a protein (LowSA).
Figure 3. Wildtype complexes ΔG model applied to mutant complexes, MinimalHighSA. The ΔG model fit to wildtype complexes, with Locked interfacial sidechains and ΔG_{ROTTRANS }= 0 applied to mutant complexes, all calculations with MinimalHighSA packing (R^{2 }= 0.66).
Repacking sidechains with the meanfield algorithm
Figure 4 shows the scheme for generation of mutant structures, using the various sidechain packing schemes that are available, Minimal or Complete and HighSA or LowSA. The previous Results sections referred to MinimalHighSA. Following the observation that buried nonpolar ASA dominates ΔG, but not ΔΔG (with MinimalHighSA binding models), we now consider the effect of using CompleteLowSA repacking. We theorise that in models of mutant structures, particularly those with replacement by alanine, sidechains will relax into the space left by the mutation. Since there may be different constraints on such relaxation in the complexed and uncomplexed states, this could lead to changes in buried area.
Figure 4. Scheme for generation of mutant complexes and different sidechain packing.
The potential for LowSA prediction is shown with the wildtype complexes in Figure 5(a), where the total ASA values are shown for: experimental structures, CompleteHighSA repacking and CompleteLowSA repacking. LowSA gives an overall result more in accord with experiment. Figure 5(b) shows an example for the barnasebarstar complex (1b27, [26]), where more sidechains packed with CompleteHighSA protrude from the crystal structure molecular surface, than do those packed with CompleteLowSA. In terms of predicted buried ASAs (polar and nonpolar combined), Figure 5(c) shows that for the set of mutants used in this study, CompleteLowSA repacking gives consistently more burial than does CompleteHighSA. This result holds when mutant systems are differenced to wildtype, and also whether the mutants are to alanine or other amino acids (not shown). Therefore the ΔΔG_{ASANP }and ΔΔG_{ASAP }terms are larger (for a given weighting) with CompleteLowSA packing than with CompleteHighSA, and we next examined whether this alters the discrepancy between ΔG and ΔΔG models.
Figure 5. CompleteHighSA and CompleteLowSA sidechain packing compared. (a) Total ASA for wildtype complexes, calculated for the experimental structures (wildtype), and repacking of all sidechains in the CompleteHighSA and CompleteLowSA schemes. (b) Molecular surface of experimental structure (1b27 subunits A and D) for barnase (green) – barstar (pink), with CompleteHighSA (red) and CompleteLowSA (blue) repacked sidechains protruding. Drawn with the program SwissPdbViewer [48]. (c) Correlation between Δ(ASA) (total buried surface area) in the complexes for CompleteHighSA and CompleteLowSA repacking (R^{2 }= 0.91).
Combining ΔG and ΔΔG binding models (CompleteLowSA sidechain repacking)
Table 2 lists the best fit models for CompleteLowSA packing applied to the wildtype complexes. The "Complete" packing schemes allow for sidechain relaxation between complexed and uncomplexed forms, including sidechain repacking in the experimentallydetermined structure of the complex. Generally sidechains away from the interface will pack similarly in the CompleteLowSA scheme in complexed and uncomplexed forms, therefore cancelling in the binding calculations. The ΔG models for CompleteLowSA are not very different from those for MinimalHighSA. Models using Locked or Unlocked interfacial sidechains for the rotameric entropy estimation are almost identical for CompleteLowSA. Also, the differences between ΔG_{ROTTRANS }= 0 and ΔG_{ROTTRANS }= 10 calculations are again small (not shown).
Figure 6 shows the bestfit CompleteLowSA ΔG binding model, derived for wildtype complexes, applied to ΔG data for mutant complexes (with all molecules repacked in the CompleteLowSA scheme). This is for rotameric entropy estimated from Locked sidechains at the interface, although the low weighting in the model means this will have little influence, and with ΔG_{ROTTRANS }= 0. Figure 6 can be compared directly with Figure 3 (the equivalent MinimalHighSA calculation), and it can be seen that these plots are qualitatively similar. We had hypothesised that the increase in buried nonpolar surface area for CompleteLowSA over MinimalHighSA models, could lead to greater consistency between ΔG and ΔΔG models. This is not the case.
Figure 6. Wildtype complexes ΔG model applied to mutant complexes, CompleteLowSA. The ΔG model fit to wildtype complexes, with Locked interfacial sidechains and ΔG_{ROTTRANS }= 0 applied to mutant complexes, all calculations with CompleteLowSA packing (R^{2 }= 0.73).
Recalculating ASA at lower solvent probe radius
Since ΔG_{ASANP }drives agreement for ΔG models, but not for ΔΔG models (whichever sidechain packing is used), we looked more closely at this property in the mutant interfaces. From Figure 7(a), (b) it is apparent that both MinimalHighSA and CompleteLowSA schemes give a spread of ΔΔ(ASANP) values around zero, albeit with larger magnitude in the CompleteLowSA scheme. Since ΔΔG_{EXP }is almost exclusively of one sign, it is clear that ΔΔG_{ASANP }will be downweighted in a best fit linear model. Figure 7(c) shows that the dual sign spread of ΔΔ(ASANP) is largely negated when the solvent probe radius is reduced from 1.4 Å to 0.5 Å, but the correlation with ΔΔG_{EXP }remains poor. These results indicate that ΔΔG_{ASANP}, with the current repacking schemes, is not an effective feature with which to understand ΔΔG binding models. Visual inspection (not shown) reveals that relatively large nonpolar surfaces may be revealed upon mutation, and whether or not these are solvent accessible depends on the fine detail of packing differences between a complex and its components. Whereas ASANP is the most prominent feature in ΔG models, either it is not an appropriate description for interfacial relaxation in response to mutation, or current modelling of interfacial relaxation is insufficient.
Figure 7. ΔΔ(ASANP) does not correlate with ΔΔG_{EXP}, and is of variable sign. (a) ΔΔ(ASANP) calculated with MinimalHighSA packing does not correlate with ΔΔG_{EXP }(R^{2 }= 0.00), and can be positive or negative (red line drawn at ΔΔ(ASANP) = 0). (b) Qualitatively similar behaviour to that for panel (a) is seen for CompleteLowSA repacking (R^{2 }= 0.02). (c) Reducing the solvent probe radius from 1.4 Å to 0.5 Å gives mostly uniform sign of ΔΔ(ASANP), but still poor correlation with ΔΔG_{EXP }(R^{2 }= 0.18).
Volumebased solvation
We reasoned that a volumebased solvation function would be less sensitive to the details of packing changes than a solvent accessible areabased feature. This is consistent with the more prominent role played by ΔG_{IONISDESOLV }in ΔΔG models, as opposed to ΔG models. Solvation shell models have been investigated previously in the context of solute/protein structure and stabilisation [2729]. Here we develop simple properties to replace Δ/ΔΔG_{ASANP }and Δ/ΔΔG_{ASAP }in the binding models, in which solvation shell volumes are calculated for each atom, on a grid. The volumes cover a shell of 2.8 Å thickness around atomic van der Waals radii, and are assigned polar or nonpolar according to atom type. Then Δ (complexation) and ΔΔ (mutant to wildtype and complexation differences) are calculated for G_{VOLNP }and G_{VOLP}. This model affords a rapid calculation, and volumebased features give the uniform sign behaviour expected for mutants that generally involve reduction of sidechain size (not shown), unlike the distribution of ΔΔ(ASANP) (Figure 7(a)).
Figure 8 compares MinimalHighSA models for area and volumebased features (Table 5), where models have been fit to wildtype ΔG data and calculated and plotted for the mutant ΔGs. The mutant data in both panels show an unequal distribution around the ΔG_{CALC }= ΔG_{EXP }line, since the 4 underlying systems are a subset of the 20 wildtype complexes used to generate the area and volumebased ΔG_{CALC }models. A relatively flat spread of mutant clusters for the areabased model is much less apparent with the volumebased model, indicating a more consistent modelling of variation within these clusters, although R^{2 }is not much different between the two panels of Figure 8. Further evidence of the effectiveness of volumebased modelling is seen when comparing equivalent ΔG and ΔΔG models in Tables 2 and 5. For MinimalHighSA and Locked interfacial sidechains, feature weights change entirely between ASAbased ΔG and ΔΔG models (e.g. with the nonpolar ASA term going from dominating to being insignificant). For volumebased models, it is actually the polar term that is more important, but this is maintained on moving from ΔG to ΔΔG. Weight variations for ΔG and ΔΔG models with CompleteLowSA repacking are more complex.
Figure 8. ASAbased and volumebased solvation ΔG models compared. Calculations for ΔG of mutant complexes, using ΔG models fit to wildtype complex data, with ΔG_{SCROT }calculated for Locked interfacial sidechains, MinimalHighSA repacking and ΔG_{ROTTRANS }= 0. (a) ASAbased polar and nonpolar solvation terms (R^{2 }= 0.66). (b) Volumebased solvation (R^{2 }= 0.68). Although there is little difference in R^{2}, the spread in ΔG_{CALC }within mutant systems (i.e. based on the same wildtype) is larger with volume calculations.
Table 5. Weights for volumebased binding models.
Looking at calculations with MinimalHighSA repacking, it appears that even simple volume calculations are capturing common properties in the ΔG and ΔΔG processes, a behaviour that has largely defeated the ASAbased calculations. The volumebased terms are particularly rapid to calculate, and could provide the basis for simple, low resolution, computational screens of interface viability. Table 6 shows ΔG and ΔΔG models derived using only two volumebased solvation terms. The R^{2 }values for MinimalHighSA models with just two features are close to those of the best fits for the more extensive MinimalHighSA models given in Table 5.
Table 6. Weights for binding models with only volumebased features.
Our investigation of simple, empirical models for binding that can generalise between ΔG and ΔΔG applications, contrasts with interfacespecific methods using quantitative structureactivity relationships that highlight residues of particular importance [31]. In practice both approaches have the same overall aim, i.e. predictive capability for proteinprotein interactions; and the same constraints, with sets of correlated features (Tables 3 and 4) and an imprecise understanding of the underlying conformational and energetic framework. Our observation that volumebased terms perform better than areabased terms in ΔΔG models highlights this latter problem. It is possible that modified areabased terms, for example with conformational sampling and weighting, could improve performance.
Conclusion
We find that binding models, using minimal sidechain repacking and ASAbased solvation terms, are quite different depending on whether they are fit to data for ΔG (wildtype complexes) or ΔΔG (modelled mutant complexes differenced to wildtype complexes). Whereas buried nonpolar area dominates the ΔG model (Figure 1, Table 2), consistent with previous work [17], other interactions assume much greater importance for the mutant complexes (Figure 2, Table 2), and the ΔG binding model does not reproduce the spread of ΔG_{EXP }within mutant sets (Figure 3).
Investigating whether different sidechain repacking could alter this discrepancy, a scheme for packing sidechains towards protein structure has been derived from a meanfield framework (Figure 4). This method, which we label CompleteLowSA since all sidechains (mutated or not) are repacked, is promising in terms of a better agreement with total ASA for experimental complexes, and in giving larger buried surface areas upon complexation than the MinimalHighSA scheme (Figure 5). However, this does not lead to significant increase in the importance of nonpolar buried area in best fit ΔΔG models, and there remains a discrepancy between ΔG and ΔΔG models (Figure 6). Further analysis of ΔΔ(ASANP) revealed a spread around zero that mitigates against fitting to ΔΔG_{EXP}, which is predominantly single sign (Figure 7). These results indicate that either nonpolar buried area is not important for ΔΔG modelling, which would be surprising given its role in ΔG modelling, or that we are not capturing the complexity of sidechain (and potentially mainchain) conformational rearrangement upon mutation.
Of the features studied, ionisable groupbased electrostatics contributes relatively little in best fits to experimental data, for both ΔG and ΔΔG models. Clearly there will be instances where ionisable groups will contribute substantially to interfacial energetics, and mediate processes such as a physiological pHdependence of binding. In general though, studies of optimal predictors of interfacial propensity show that net charge is (in relative terms) excluded, part of an overall tendency for ease of desolvation at interfaces [30]. For most ΔG and ΔΔG models, sidechain rotameric entropy plays a relatively small part (Table 2), and where the weight is large may be partly due to correlations with other properties (Tables 3, 4). In ΔΔG models with ASAbased solvation, ΔΔG_{ASAP }and ΔΔG_{IONISDESOLV }assume more importance. Polar solvation may be reflecting overall burial change in the interface upon mutation, rather than indicative of particular favourable polar interactions. The effects of mutations on polar area relative to nonpolar area are somewhat different. The polar area equivalent to the nonpolar area data plotted in Figure 7(a) (MinimalHighSA) is qualitatively similar, whereas the polar area equivalent to Figure 7(b) (CompleteLowSA) is qualitatively different, being largely of a single sign (not shown).
Empirical desolvation for ionisable groups, describing an estimate of the entropy of water molecule liberation, is a simple volumebased term. We therefore tested the capacity for volumebased terms in general to account for solvation changes in ΔΔG models, in place of areabased terms. The volume solvation features assume importance in all models, reducing the discrepancy between ΔG and ΔΔG models (Figure 8). Volumebased models are part of the molecular mechanics forcefields in some applications [20,29], and ΔΔG models with volumebased solvation terms have been used, in part for faster calculation [19,20]. In the current work, we show that even a very simple solvation shell model is effective in improving consistency of ΔG and ΔΔG models. Surface areabased modelling for ΔΔG fails since ASA is particularly sensitive to relatively small conformational changes, even for single site mutations. In contrast volume based models are less sensitive, and a simple binding model for ΔG and ΔΔG can be constructed with just polar and nonpolar volumebased features. This could be useful in computational assessment of the validity of comparative modelled interfaces, and our simple implementation is made available for such analyses.
Methods
Binding data and protein structures
Protein complexes were selected where the literature and structural databases give no evidence of major conformational change in the mainchain upon complexation, and for which measured ΔG is available. The literature e.g. [31] and various databases were used to search for binding energies associated with complexation, the alanine scanning energetics database (ASEdb, [32]), the proteinprotein interactions thermodynamic database (PINT, [33]), and the ProTherm thermodynamic database for proteins and mutants [34]. Imposition of limited conformational change led to the inclusion of just 20 complexes, which are listed in Table 1 with their measured binding energies. In cases where binding data are recorded for multiple conditions, that most closely corresponding to our calculation conditions of 300 K, 0.15 M ionic strength, pH 7, were chosen. The data in Table 1 were used to construct ΔG binding models. In calculations, only structure files (from the PDB, [4]) for the complex were used. All components (free proteins and mutated proteins) were derived from these coordinates.
For mutant data in ΔΔG model fitting, 4 of the systems used in ΔG modelling were included. The restriction of no major mainchain changes was therefore carried over to the mutants ΔΔG analysis. These systems, and the number of mutants associated with each, are: barnasebarstar, 64 mutants; chymotrypsinBPTI, 15 mutants; ralGDSras, 49 mutants; trypsinBPTI, 15 mutants. Where mutants are solely changes to alanine, no repacking is required in the MinimalHighSA or MinimalLowSA schemes. CompleteHighSA and CompleteLowSA schemes will repack all sidechains.
Binding model
We employed an empirical binding model with contributions from the rigid body rotational and translational entropy of complexation (ΔG_{ROTTRANS}), buried nonpolar surface area (ΔG_{ASANP}), buried polar surface area (ΔG_{ASAP}), ionisable group charge interactions (ΔG_{IONISFDDH}), a term to approximate the free energy of water molecule liberation upon ionisable group burial (ΔG_{IONISDESOLV}), and sidechain rotameric entropy (ΔG_{SCROT}). Thus;
where the various premultipliers (w) are the weights to be adjusted in model fitting to experimental data. More detail follows for the individual terms.
The rotational and translational entropy change associated with complexation of two rigid bodies has been studied experimentally and theoretically [25,35,36]. Measurements suggest that an entropy penalty corresponding to a free energy in the range of 0–10 kJ per mole of interacting species at 300 K is appropriate [25]. This is a relatively small range compared with measured ΔG values (Table 1). Other computational work has set ΔG_{ROTTRANS }to zero [8]. We examine ΔG_{ROTTRANS }at either 0 or 10 kJ/mole for each binding model, to test the sensitivity of the model to this term. Models calculated at these ΔG_{ROTTRANS }values, for a given set of conditions, are very similar (Table 2), so that the precise value is not a major consideration in this study. We are neglecting the entropic term associated with any changes in vibrational modes upon complexation [37].
Nonpolar and polar solvent accessible surface areas are calculated with the program SACALC, developed in our laboratory. Areas are then differenced between a complex and the sum of its components, and multiplied by a factor of 0.1 kJ/mole/Å^{2}. This factor is within the range generally assumed to represent the energetics of hydrophobic solvation in empirical modelling [38,39]. The precise value is not critical, since linear fitting will scale surface area terms via the premultipliers. The same factor of 0.1 has been used for polar surface area, and we include this feature in part to allow for some approximate recognition of hydrogenbonding potential. Detailed assessment of pairwise hydrogen bonds, outside of the context of ionisable groups, is not included. Additionally, explicit van der Waals interactions are excluded. Both hydrogen bond and van der Waals interactions, with a strong distancedependence over fractions of an Å, would be more appropriate if energy minimisation were carried out subsequent to sidechain repacking from a discrete rotamer library. We chose to develop binding models without energy minimisation, and this relatively simple approach gives a broad insight into differences between ΔG and ΔΔG models. Both the nonpolar and polar area terms, as defined, are favourable for complexation when weights are positive.
Ionisable group interactions were derived from the pHdependence of electrostatic energy, with addition of a constant of integration at an extreme pH [40]. The pHdependent electrostatics were calculated with inhouse programs using the FD/DH method that combines Finite Difference PoissonBoltzmann (FDPB, [41]) and DebyeHûckel (DH) interaction schemes [42]. Monte Carlo sampling [43] was used to derive pKas [44] and the ionisable charge distribution, from which electrostatic energy is obtained [45]. Ionisable group energies are included with the ΔG_{IONISFDDH }term, and may be either favourable or unfavourable for complexation.
We have previously introduced an empirical term to account for the entropy of water liberation upon ionisable group burial, using a comparison of calculated and measured pKas [46]. This analysis looked at hydration differences between ionised and neutral states. The significance of this empirical parameter in pKa calculations was generally small, which was rationalised in terms of little overall difference between water ordering in the ionised and neutral states. Cysteine was an exception, consistent with relatively little charge separation and reduced hydrogenbonding potential in the neutral state. The ΔG_{IONISDESOLV }term in the current study models change in burial of ionisable groups upon complexation, rather than ionised/neutral form differences. In order to model the entropy associated with hydration shell liberation (desolvation) for ionisable groups, we used the derived cysteine value from our previous work, since in this case the neutral form has relatively little charge separation. Then ΔG_{IONISDESOLV }is this complete hydration shell value multiplied by the change in hydration shell volume (calculated from FDPB grids) upon complexation, with no other variation between ionisable group types. As with other terms, the weight derived by fitting to experimental data will indicate relative importance. With liberation of solvating water upon complexation, this term is expected to be favourable for binding.
Finally in the binding scheme is modelling of free energy changes due to alteration of sidechain rotameric entropy upon complexation, ΔG_{SCROT}. We use a method based on meanfield packing of sidechains, with derived probabilities (p) for rotamers based on packing opportunities [21,22]. Sidechain rotameric entropy for each amino acid is the sum over p*ln(p) for rotamers. Values are summed over amino acids in a protein, differenced between free and complexed states, and multiplied by RT = 2.5 kJ/mole to give a free energy contribution, prior to weighting by the premultiplier. Changes in sidechain rotameric entropy are expected to be unfavourable for complexation (restriction of sidechains).
We used two variations of the sidechain rotamer term. In the first, rotamer packing differences upon complexation are calculated as described, with interfacial sidechains free to explore different packings, even though energy calculation for other terms is based on a single conformer. This variation is termed "Unlocked". In the second, interfacial sidechains (in the complex) are modelled as fixed in the conformation used for other components of the energy calculation. Entropy changes will therefore be larger for the second case, which is described as "Locked". These differences are discussed in the Results section, although generally the impact of the sidechain rotameric entropy was low in the models, whichever scheme was used for interfacial flexibility.
Binding differences model
We simply difference the binding model between wildtype and mutant systems (ΔΔG_{EXP }= ΔG_{EXP }[MUT]  ΔG_{EXP }[WT]), with the rigidbody rotation and translation term cancelling. A prime has been added to the weights, demonstrating that we are allowing different fits for ΔG and ΔΔG models.
Model fitting
Multiple linear regression was used to determine the best fit ΔG_{CALC }and ΔΔG_{CALC }models to experiment. This regression was performed with the builtin least squares function of the GNU Regression, Econometrics and Timeseries Library package (GRETL, [47]). The Solver function in Microsoft Excel was also used to carry out linear regression. Weights are expected to be positive to make physical sense, other than for ΔG_{IONISFDDH}, which could be of either sign with attractive or repulsive interactions to the fore.
Sidechain repacking
Starting with an experimental structure for a wildtype complex, there are questions of conformational change and repacking for the uncomplexed components and mutated proteins. Data selection should have eliminated systems with largescale mainchain conformational changes, but sidechain rearrangement remains an issue.
The basis of our methodology is a meanfield program developed [21] from earlier work [22]. This uses pairwise packing of rotamers to derive probabilities for rotamers within a sidechain, according to an allowed van der Waals tolerance in the packing. Higher rotamer probability means coexistence with a larger number of neighbouring sidechain rotamers, and larger solvent accessibility (HighSA). Conversely, the lower (but nonzero) probability rotamers will tend to have lower solvent accessibility (LowSA). Both of these packing schemes/rotamer selections are used in our studies of ΔG and ΔΔG models. Another question for sidechain repacking is whether to remain as close as possible to experimental (complex) structure (Minimal repacking), or whether to allow sidechain relaxations in response to complex separation and mutation (Complete repacking).
Volumebased solvation
A simple volumebased solvation function was used to replace the ASAbased analysis at some points in the work. Thus, w_{VOLNP}ΔG_{VOLNP }+ w_{VOLP}ΔG_{VOLP }was swapped into the ΔG_{CALC }equation in place of w_{ASANP}ΔG_{ASANP }+ w_{ASAP}ΔG_{ASAP}, with the analogous weighted terms also for the ΔΔG_{CALC }binding model. These volume solvation terms are based on grid calculations of volumes around nonhydrogen atoms that are filled or unfilled by neighbouring atoms. Nonpolar atoms and radii (Å) are C:2.0 and S:1.9. Polar atoms and radii are O:1.5 and N:1.8. Volumes for each atom are calculated with a 0.5 Å spaced grid and a shell of thickness 2.8 Å beyond the atomic radius. These calculations give numbers of grid points that are not covered by neighbouring atoms. In order to put the numbers onto a scale roughly equating to that for ASAbased terms, a multiplicative factor applied to the number of grid points in the solvation shell of a C atom was equated with the ASA energy for the same, unoccluded, atom. This multiplicative factor is 0.0042.
Availability and requirements
Project name: Intcalc
Project home page: http://www.bioinf.manchester.ac.uk/intcalc/ webcite
The software used in this study is also available for download from: http://personalpages.manchester.ac.uk/staff/j.warwicker/resources.html webcite
Operating system(s): Linux
Programming language: Perl, Fortran
License: GNU GPL
No additional restrictions for nonacademic users.
Abbreviations
ASA: Accessible Surface Area; PDB: Protein Data Bank; PINT: Proteinprotein Interactions Database; ASEdb: Alanine Scanning Energetics database; BPTI: Bovine Pancreatic Trypsin Inhibitor; FDPB: Finite Difference PoissonBoltzmann; DH: DebyeHückel; FD/DH: Finite Difference/DebyeHückel; GRETL: GNU Regression: Econometrics and Timeseries Library.
Authors' contributions
SB and JW conceived the study, interpreted the data and wrote the final manuscript together. SB and JW both contributed source code, whilst dataset creation and implementation of the computational analyses were due to SB.
Acknowledgements
The Algerian Ministry of Higher Education is thanked for the award of PhD funding to SB. We thank Dr Nick Gresham for technical support, and James Kitchen, Tracey Bray and Pedro Chan for discussions.
References

Auerbach D, Thaminy S, Hottiger MO, Stagljar I: The postgenomic era of interactive proteomics: facts and perspectives.
Proteomics 2002, 2:611623. PubMed Abstract  Publisher Full Text

Gingras AC, Aebersold R, Raught B: Advances in protein complex analysis using mass spectrometry.
J Physiol 2005, 563:1121. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Zhu X, Gerstein M, Snyder M: Getting connected: analysis and principles of biological networks.
Genes Dev 2007, 21:10101024. PubMed Abstract  Publisher Full Text

Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE: The Protein Data Bank.
Nucl Acids Res 2000, 28:235242. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Chandonia JM, Brenner SE: The impact of structural genomics: Expectations and outcomes.
Science 2006, 311:347351. PubMed Abstract  Publisher Full Text

Ritchie DW: Recent progress and future directions in proteinprotein docking.
Curr Protein Pept Sci 2008, 9:115. PubMed Abstract  Publisher Full Text

Vakser IA, Kundrotas P: Predicting 3D structures of proteinprotein complexes.
Curr Pharm Biotechnol 2008, 9:5766. PubMed Abstract  Publisher Full Text

Audie J, Scarlata S: A novel empirical free energy function that explains and predicts proteinprotein binding affinities.
Biophys Chem 2007, 129:198211. PubMed Abstract  Publisher Full Text

Eisenstein M, KatchalskiKatzir E: On proteins, grids, correlations, and docking.
C R Biol 2004, 327:409420. PubMed Abstract  Publisher Full Text

Vajda S, Camacho CJ: Proteinprotein docking: is the glass halffull or halfempty?
Trends Biotechnol 2004, 22(3):110116. PubMed Abstract  Publisher Full Text

Gabb HA, Jackson RM, Sternberg MJ: Modelling protein docking using shape complementarity, electrostatics and biochemical information.
J Mol Biol 1997, 272:106120. PubMed Abstract  Publisher Full Text

Althaus E, Kohlbacher O, Lenhof HP, Müller P: A combinatorial approach to protein docking with flexible side chains.
J Comput Biol 2002, 9:597612. PubMed Abstract  Publisher Full Text

SchuelerFurman O, Wang C, Baker D: Progress in proteinprotein dcking: atomic resolution predictions in the CAPRI experiment using RosettaDock with an improved treatment of sidechain flexibility.
Proteins 2005, 60:187194. PubMed Abstract  Publisher Full Text

Wang C, SchuelerFurman O, Sndre I, London N, Fleishman SJ, Bradley P, Qian B, Baker D: RosettaDock in CAPRI rounds 6–12.
Proteins 2007, 69:758763. PubMed Abstract  Publisher Full Text

Aloy P, Russell RB: Ten thousand interactions for the molecular biologist.
Nat Biotechnol 2004, 22:13171321. PubMed Abstract  Publisher Full Text

Kiel C, Beltrao P, Serrano L: Analyzing protein interaction networks using structural information.
Annu Rev Biochem 2008, 77:415441. PubMed Abstract  Publisher Full Text

Horton N, Lewis M: Calculation of the freeenergy of association for protein complexes.
Protein Science 1992, 1:169181. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Teng S, MichonovaAlexova E, Alexov E: Approaches and resources for prediction of the effects of nonsynonymous single nucleotide polymorphism on protein function and interactions.
Curr Pharm Biotechnol 2008, 9:123133. PubMed Abstract  Publisher Full Text

Guerois R, Nielsen JE, Serrano L: Predicting changes in the stability of proteins and protein complexes: a study of more than 1000 mutations.
J Mol Biol 2002, 320:369387. PubMed Abstract  Publisher Full Text

Kortemme T, Baker D: A simple model for binding energy hot spots in proteinprotein complexes.
Proc Natl Acad Sci USA 2002, 99:1411614121. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Cole C, Warwicker J: Sidechain conformational entropy at proteinprotein interfaces.
Protein Science 2002, 11:28602870. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Koehl P, Delarue M: Application of a selfconsistent mean field theory to predict protein sidechains conformation and estimate their conformational entropy.
J Mol Biol 1994, 239:249275. PubMed Abstract  Publisher Full Text

Xiang Z, Steinbach PJ, Jacobson MJ, Friesner RA, Honig B: Prediction of sidechain conformations on protein surfaces.
Proteins 2007, 66:814823. PubMed Abstract  Publisher Full Text

Canutescu AA, Shelenkov AA, Dunbrack RL Jr: A graphtheory algorithm for rapid protein sidecahin prediction.
Protein Science 2003, 12:20012014. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Tamura A, Privalov PL: The entropy cost of protein association.
J Mol Biol 1997, 273:10481060. PubMed Abstract  Publisher Full Text

Vaughan CK, Buckle AM, Fersht AR: Structural response to mutation at a proteinprotein interface.
J Mol Biol 1999, 286:14871506. PubMed Abstract  Publisher Full Text

Kang YK, Nemethy G, Scheraga HA: Free energies of hydration of solute molecules 1. Improvement of the hydration shell model by exact computations of overlap volumes.
J Chem Phys 1987, 91:41054109. Publisher Full Text

ColonnaCesari F, Sander C: Excluded volume approximation to proteinsolvent interaction. The solvent contact model.
Biophys J 1990, 57:11031107. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Lazaridis T, Karplus M: Effective energy function for proteins in solution.
Proteins 1999, 35:133152. PubMed Abstract  Publisher Full Text

Burgoyne NJ, Jackson RM: Predicting protein interaction sites: binding hotspots in proteinprotein and proteinligand interfaces.
Bioinformatics 2006, 22:13351342. PubMed Abstract  Publisher Full Text

Wang T, Tomic S, Gabdoulline RR, Wade RC: How optimal are the binding energetics of barnase and barstar?
Biophys J 2004, 87:16181630. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Thorn KS, Bogan AA: ASEdb: a database of alanine mutations and their effects on the free energy of binding in protein interactions.
Bioinformatics 2001, 17:284285. PubMed Abstract  Publisher Full Text

Kumar MD, Gromiha MM: PINT: Proteinprotein Interactions Thermodynamic Database.
Nucl Acids Res 2006, 34:D195D198. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Bava KA, Gromiha MM, Uedaira H, Kitajima K, Sarai A: ProTherm, version 4.0; thermodynamic database for proteins and mutants.
Nucl Acids Res 2004, 32:D120D121. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Finkelstein AV, Janin J: The price of lost freedom: the entropy of bimolecular complex formation.
Protein Eng 1989, 3:13. PubMed Abstract  Publisher Full Text

Amzel LM: Loss of translational entropy in binding, folding, and catalysis.
Proteins 1997, 28:144149. PubMed Abstract  Publisher Full Text

Gohlke H, Case DA: Converging free energy estimates: MMPB(GB)SA studies on the proteinprotein complex RasRaf.
J Comput Chem 2004, 25:238250. PubMed Abstract  Publisher Full Text

Reynolds JA, Gilbert DB, Tanford C: Empirical correlation between hydrophobic free energy and aqueous cavity surface area.
Proc Natl Acad Sci USA 1974, 71:29252927. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Lee B: Calculation of volume fluctuations for globular protein models.
Proc Natl Acad Sci USA 1983, 80:622626. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Chan P, Lovric J, Warwicker J: Subcellular pH and the predicted pHdependent features of proteins.
Proteomics 2006, 6:34943501. PubMed Abstract  Publisher Full Text

Warwicker J: Continuum dielectric modelling of the proteinsolvent system, and calculation of the longrange electrostatic field of the enzyme phosphoglycerate mutase.
J Theor Biol 1986, 121:199210. PubMed Abstract  Publisher Full Text

Warwicker J: Improved pKa calculations through flexibility based sampling of a waterdominated interaction scheme.
Protein Science 2004, 13:27932805. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Beroza P, Fredkin DR, Okamura MY, Feher G: Protonation of interacting residues in a protein by a Monte Carlo method: application to lysozyme abd the photosynthetic reaction center of Rhodobacter sphaeroides.
Proc Natl Acad Sci USA 1991, 88:58045808. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Bashford D, Karplus : pKa's of ionisable groups in proteins: atomic detail from a continuum electrostatic model.
Biochemistry 1990, 29:1021910225. PubMed Abstract  Publisher Full Text

Antosiewicz J, McCammon JA, Gilson MK: Prediction of the pHdependent properties of proteins.
J Mol Biol 1994, 238:415436. PubMed Abstract  Publisher Full Text

Warwicker J: Improving pKa calculations with consideration of hydration entropy.
Protein Eng 1997, 10:809814. PubMed Abstract  Publisher Full Text

Gnu Regression, Econometrics and Timeseries Library [http://gretl.sourceforge.net/] webcite

Guex N, Peitsch MC: SwissModel and the SwissPdbViewer: an environment for comparative protein modelling.
Electrophoresis 1997, 18:27142723. PubMed Abstract  Publisher Full Text

Castro MJM, Anderson S: Alanine pointmutations in the reactive region of bovine pancreatic trypsin inhibitor: Effects on the kinetics and thermodynamics of binding to betatrypsin and alphachymotrypsin.
Biochemistry 1996, 35:1143511446. PubMed Abstract  Publisher Full Text

Frisch C, Schreiber G, Johnson CM, Fersht AR: Thermodynamics of the interaction of barnase and barstar: changes in free energy versus changes in enthalpy on mutation.
J Mol Biol 1997, 267:696706. PubMed Abstract  Publisher Full Text

Horn JR, Ramaswamy S, Murphy KP: Structure and Energetics of ProteinProtein Interactions: The Role of Conformational Heterogeneity in OMTKY3 Binding to Serine Proteases.
J Mol Biol 2003, 331:497508. PubMed Abstract  Publisher Full Text

Herrmann C, Horn G, Spaargaren M, Wittinghofer A: Differential Interaction of the Ras Family GTPbinding Proteins HRas, Rap1A, and RRas with the Putative Effector Molecules Raf Kinase and RalGuanine Nucleotide Exchange Factor.
J Biol Chem 1996, 271:67946800. PubMed Abstract  Publisher Full Text

Wohlgemuth S, Kiel C, Krämer A, Serrano L, Wittinghofer F, Herrmann C: Recognizing and Defining True Ras Binding Domains I: Biochemical Analysis.
J Mol Biol 2005, 348:741758. PubMed Abstract  Publisher Full Text

Dall'Acqua W, Goldman ER, Eisenstein E, Mariuzza RA: A mutational analysis of the binding of two different proteins to the same antibody.
Biochemistry 1996, 35:96679676. PubMed Abstract  Publisher Full Text

Verhoeyen M, Milstein C, Winter G: Reshaping human antibodies: Grafting an antilysozyme activity.
Science 1988, 239:15341536. PubMed Abstract  Publisher Full Text

Rajpal A, Taylor MG, Kirsch JF: Quantitative evaluation of the chicken lysozyme epitope in the HyHEL10 Fab complex: Free energies and kinetics.
Protein Science 1998, 7:18681874. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Kiel C, Serrano L, Herrmann C: A Detailed Thermodynamic Analysis of Ras/Effector Complex Interfaces.
J Mol Biol 2004, 340:10391058. PubMed Abstract  Publisher Full Text

Ascenzi P, Amiconi G, Menegatti E, Guarneri M, Bolognesi M, Schnebli HP: Binding of the recombinant proteinase inhibitor eglin c from leech Hirudo medicinalis to human leukocyte elastase, bovine alphachymotrypsin and subtilisin Carlsberg: Thermodynamic study.
J Enzyme Inhib 1988, 2(3):167172. PubMed Abstract  Publisher Full Text

Wallis R, Leung KY, Osborne MJ, James R, Moore GR, Kleanthous C: Specificity in ProteinProtein Recognition: Conserved Im9 Residues Are the Major Determinants of Stability in the Colicin E9 DNaseIm9 Complex.
Biochemistry 1998, 37:476485. PubMed Abstract  Publisher Full Text

Lavoie TB, Drohan WN, SmithGill SJ: Experimental analysis by sitedirected mutagenesis of somatic mutation effects on affinity and fine specificity in antibodies specific for lysozyme.
J Immunol 1992, 148:503513. PubMed Abstract  Publisher Full Text

Read RJ, Fujinaga M, Sielecki AR, James MNG: Structure of the complex of Streptomyces griseus protease B and the third domain of the turkey ovomucoid inhibitor at 1.8 Å resolution.
Biochemistry 1983, 22:44204433. PubMed Abstract  Publisher Full Text

Shapiro R, RuizGutierrez M, Chen CZ: Analysis of the interactions of human ribonuclease inhibitor with angiogenin and ribonuclease A by mutagenesis: Importance of inhibitor residues inside versus outside the Cterminal 'hot spot'.
J Mol Biol 2000, 302:497519. PubMed Abstract  Publisher Full Text

Kortt AA, Nice E, Gruen LC: Analysis of the Binding of the Fab Fragment of Monoclonal Antibody NC10 to Influenza Virus N9 Neuraminidase from Tern and Whale Using the BIAcore Biosensor: Effect of Immobilization Level and Flow Rate on Kinetic Analysis.
Anal Biochem 1999, 273:133141. PubMed Abstract  Publisher Full Text

Uehara Y, Tonomura B, Hiromi K: Direct fluorometric determination of a dissociation constant as low as 10–10 M for the subtilisin BPN'protein proteinase inhibitor (Streptomyces subtilisin inhibitor) complex by a single photon counting technique.
J Biochem 1978, 84:11951202. PubMed Abstract  Publisher Full Text

Pineda AO, Cantwell AM, Bush LA, Rose T, Cera ED: The thrombin epitope recognizing thrombomodulin is a highly cooperative hot spot in exosite I.
J Biol Chem 2002, 277:3201532019. PubMed Abstract  Publisher Full Text

Chen Z, Bode W: Refined 2·5 Å Xray crystal structure of the complex formed by porcine kallikrein A and the bovine pancreatic trypsin inhibitor. Crystallization, Patterson search, structure determination, refinement, structure and comparison with its components and with the bovine trypsinpancreatic trypsin inhibitor complex.
J Mol Biol 1983, 164:283311. PubMed Abstract  Publisher Full Text