Thermodynamic Basis of Selectivity in the Interactions of Tissue Inhibitors of Metalloproteinases N-domains with Matrix Metalloproteinases-1, -3, and -14

Abstract

The four tissue inhibitors of metalloproteinases (TIMPs) are potent inhibitors of the many matrixins (MMPs), except that TIMP1 weakly inhibits some MMPs, including MMP14. The broad-spectrum inhibition of MMPs by TIMPs and their N-domains (NTIMPs) is consistent with the previous isothermal titration calorimetric finding that their interactions are entropy-driven but differ in contributions from solvent and conformational entropy (ΔS_solv, ΔS_conf), estimated using heat capacity changes (ΔC_p). Selective engineered NTIMPs have potential applications for treating MMP-related diseases, including cancer and cardiomyopathy. Here we report isothermal titration calorimetric studies of the effects of selectivity-modifying mutations in NTIMP1 and NTIMP2 on the thermodynamics of their interactions with MMP1, MMP3, and MMP14. The weak inhibition of MMP14 by NTIMP1 reflects a large conformational entropy penalty for binding. The T98L mutation, peripheral to the NTIMP1 reactive site, enhances binding by increasing ΔS_solv but also reduces ΔS_conf. However, the same mutation increases NTIMP1 binding to MMP3 in an interaction that has an unusual positive ΔC_p. This indicates a decrease in solvent entropy compensated by increased conformational entropy, possibly reflecting interactions involving alternative conformers. The NTIMP2 mutant, S2D/S4A is a selective MMP1 inhibitor through electrostatic effects of a unique MMP-1 arginine. Asp-2 increases reactive site polarity, reducing ΔC_p, but increases conformational entropy to maintain strong binding to MMP1. There is a strong negative correlation between ΔS_solv and ΔS_conf for all characterized interactions, but the data for each MMP have characteristic ranges, reflecting intrinsic differences in the structures and dynamics of their free and inhibitor-bound forms.

Introduction

Isothermal titration calorimetry can dissect the sources of the free energy changes for protein interactions with other macromolecules and ligands (1). Measurements of the heat released or absorbed during the titration of a protein with a binding partner can quantify the enthalpy of binding (ΔH), association constant K_a, and stoichiometry (N) (1), allowing the calculation of the changes in free energy (ΔG) and entropy (ΔS) of binding. Titrations in buffers with different enthalpies of ionization quantify ionization changes linked to binding, whereas the heat capacity change for binding, ΔC_p, measured as the temperature dependence of ΔH, can be used to estimate the change in solvation entropy on binding (ΔS_solv). These parameters can be correlated with the character of the interaction interface and differences in dynamics and solvation between the free and bound conformer populations (2–4).

Previously, we used isothermal titration calorimetry to elucidate the thermodynamic profiles of interactions between the N-terminal inhibitory domains of tissue inhibitors of metalloproteinases-1 and -2 (NT1 and NT2)³ and the catalytic domains of matrix metalloproteinases -1 and -3 (MMP1c and MMP3c) (5, 6). TIMP1 and TIMP2 are two of the four human TIMPs, endogenous, broad spectrum, slow binding, high affinity inhibitors of the 23 human MMPs and several disintegrin-metalloproteinases (7). The MMPs catalyze the proteolysis of all polypeptide components of the extracellular matrix and are crucial for tissue remodeling, wound healing, embryo implantation, cell migration, shedding of cell surface proteins, and release of bioactive peptides (8, 9); the unregulated activities of various MMPs have been linked to many disease processes including arthritis, heart disease, and tumor metastasis (8).

The two domains of vertebrate TIMPs are each cross-linked by three disulfide bonds. The larger N-terminal domain (NTIMP) carries the MMP inhibitory activity, and the C-terminal domain mediates interactions with other proteins, including some pro-MMPs (7). Recombinant forms of NTIMPs are fully active as MMP inhibitors (10) and have been extensively used in crystallographic (11–12), mutational (13–18), and NMR studies (10, 19–22) of TIMP·MMP interactions. The known structures of complexes between full-length TIMPs and MMP catalytic domains show that the main interaction interface of the TIMP is provided by the N-domain with a few peripheral contacts from the C-domain (11, 12, 23–27). N-TIMPs have an oligonucleotide/oligosaccharide-binding fold, a 5-stranded β-barrel structure with two small helices. The core of the MMP-binding site of TIMP is a surface ridge formed by the N-terminal five residues, ¹C(T/S)C(V/A/S)P⁵ and the connector between β-strands C and D, residues that are linked by the Cys-1 to Cys-70 disulfide bond (7, 23–25). As shown in Fig. 1, this region is oriented in the active site of the MMP so that the α-amino group and carbonyl oxygen of Cys-1 coordinate the catalytic zinc (11, 12, 23–28). When the α-amino group is chemically modified or extended by an N-terminal alanine, the MMP inhibitory activity is essentially eliminated (17, 29–30). The side chain of TIMP residue 2 (Ser or Thr) sits over the mouth of the S₁′ subsite (the “specificity pocket”) of the MMP active site (11, 12, 23–28), and eliminating the side chain by substitution with glycine greatly weakens the affinity for most, but not all, MMPs (13, 14). Residues 3–5 interact with the S2′ and S3′ subsites, and the C-D β-strand connector interacts with the MMP S2 and S3 subsites (Fig. 1). Loops between β-strands A and B and strands E and F and the C-terminal end of β-strand D make variable contributions in different TIMP·MMP complexes (11, 12, 23–28). The A-B loop of NT2 includes seven more residues than that of NT1 and has multiple interactions with the MMP in its complexes with MMP14 (MT1·MMP), MMP13c, and MMP10c (24, 25, 27, 28) that are absent from complexes of TIMP-1 with MMP1c, MMP3c, or MMP10c (11, 23, 27).

FIGURE 1.

A schematic view of the interactions between the core of the NT1 interaction ridge and the active site and substrate binding subsites of MMP1. The N-terminal five residues of TIMP-1 are colored cyan, residues 67–70 and 98–99 are gray, the Cys-1–Cys-70 and Cys-3–Cys-99 disulfide bonds are yellow, oxygen atoms are red, and nitrogen atoms are blue. Residues 214–221 of MMP1 are represented by the blue ribbon, and the catalytic Zn²⁺ is represented by a purple sphere.

TIMP-3 inhibits more metalloproteinases than the other TIMPs, including disintegrin-metalloproteinases such as ADAM-17 (a disintegrin and metalloproteinase-17), ADAMTS-4 (a disintegrin and metalloproteinase with thrombospondin domains), and ADAMTS-5 (7), and these interactions are affected differently from those with MMPs by mutations in its reactive site (17, 31). The specificity of N-TIMPs for MMPs can also be modified by protein engineering to produce variants with enhanced or reduced selectivity for MMPs (13–18) and have potential applications treating diseases linked to excess MMP activities. Previously, we identified NT2 variants that inhibit MMP1 preferentially over MMP3 using phage display in conjunction with positive and negative selection with MMP1c and MMP3c, respectively (18). MMP1 (fibroblast collagenase) and MMP3 (stromelysin 1) have been validated as a target and anti-target for cancer therapy mediated by MMP inhibition (32). The most selective mutant, S2D/S4A, has a nanomolar K_i for MMP-1 but does not inhibit MMP3c or MMP14c and weakly inhibits MMP2c, MMP7c, MMP8c, and MMP13c (18). Although other TIMPs are high affinity inhibitors of all MMPs, TIMP-1 is a poor inhibitor of the membrane-type MMPs (MMP14, MMP16, and MMP24) and MMP19. The T98L substitution in NT1 has been shown to enhance its affinity for MMP14 (2–3-fold), and additional substitutions, V4A and P6V, increase the affinity, reflected in a 10-fold improvement of the K_i in the triple mutant (15, 14). A crystallographic structure of the complex of the triple mutant of NT1 with MMP14 has been determined (26).

Here, we have investigated how the mutations in NT1 and NT2 that modify MMP selectivity affect the thermodynamics of N-TIMP·MMP interactions, focusing on the T98L mutation in NT1 with MMP3c and MMP14c and the S2D/S4A double substitution in NT2 (with MMP1c). The thermodynamic profiles of the interactions of these MMPs with WT NT1 and NT2 (6) show that all are driven by entropy increases. Entropy-driven binding has been observed in other proteins that bind to multiple targets, including thioredoxin and protein kinase A (33, 34). The solvent entropy change for the interaction, ΔS_solv, can be estimated from the heat capacity change, ΔC_p (35). Using ΔS_solv and ΔS_int, the conformation entropy change for the interaction (ΔS_conf) can be determined to provide information about differences in conformational dynamics between the free and bound forms of the two proteins. The results highlight the contributions of changes in conformational dynamics and solvent entropy (the hydrophobic effect) to differences in binding to different MMPs.

Experimental Procedures

Construction, Expression, Purification, and Folding of NT2 Variants, MMP1c, and MMP3c

Reagents and cells were from the same sources as in previous studies (5, 6, 24–27, 29, 31). The NT1 and NT2 mutants were generated using QuikChange II Site-Directed Mutagenesis kits (Agilent Technologies). Primers were designed using web-based primer design software program (Agilent Technologies). PCR reactions were carried out at 95 °C for 30 s, 55 °C for 1 min, and 68 °C for 5 min for 30 cycles after a 3-min hot start at 95 °C. The PCR products were cloned back into pET-42b vector (Novagen) for expression.

NT2 variants were extracted from inclusion bodies and folded as described previously (6). The native proteins were purified by ion exchange followed by gel filtration with columns (2.5 × 35 cm) of Superdex-75 (Amersham Bioscience), equilibrated, and eluted with 20 mm HEPES buffer, pH 7.4, containing 250 mm NaCl and 20 mm CaCl₂. The eluate was collected in 6-ml fractions at a flow rate of 0.5 ml/min. Fractions containing folded N-TIMPs were identified by polyacrylamide gel electrophoresis, pooled, and concentrated using Centriplus YM-3 centrifugal filter devices (Millipore). MMP1c and MMP3c were expressed as inclusion bodies in Escherichia coli BL21-CodonPlus® Competent Cells, folded and purified as in previous studies (6).

Fluorescence Assays for N-TIMP Activity

The inhibition of MMPs by NT2 and NT1 variants was measured by assaying MMP activities for hydrolysis of fluorogenic substrates as described previously (6, 13, 14). Assays were conducted in HEPES buffer (20 mm), pH 7.4, containing 250 mm NaCl, 10 mm CaCl₂, and 50 μm ZnCl₂, which was used also for the dilution of MMP and TIMP samples. The K_i^app of N-TIMP variants for MMP-1c and MMP-3c at 25 °C (298 K) were determined as described previously (14, 16).

Isothermal Titration Calorimetry of the Interactions of NT1 and NT2 Variants with MMPs

Protein solutions were dialyzed extensively against various buffers at 20 mm concentrations containing 250 mm NaCl, 10 mm CaCl₂, and 50 μm ZnCl₂ at pH 7.4 and degassed before use. N-TIMPs (12–30 μm) were titrated with the MMP (120–300 μm) at different temperatures using a MicroCal VP-ITC microcalorimeter as described previously (5, 6). The instrument was programmed to carry out 14 injections of 20 μl each over 40 s, spaced at 300-s intervals (see Figs. 2 and 3). The stirring speed was 300 rpm. The data were analyzed by the software package Origin 5.0 from Microcal Inc., which was used to calculate the enthalpy changes (ΔH) and stoichiometry (N) using a single-site binding model. As in previous studies, only ∼44% of the recombinant NT1 and NT2 variants were active (5, 6) reflecting inactivation by N-acetylation the N terminus by the bacterium (30). The heat capacity change (ΔC_p), intrinsic enthalpy change (ΔH_int), and ionization change (N_H+) for each interaction were calculated as described below.

FIGURE 2.

Titration of different N-TIMPs by MMP14c in HEPES buffer, pH 7.4, at 310 K. A, aliquots (20 μl) of MMP14c (120 μm) were injected into NT1 (23 μm). B, aliquots (20 μl) of MMP14c (120 μm) were injected into NT1 T98L mutant (22 μm). C, aliquots (20 μl) of MMP14c (148 μm) were injected into NT2 (16 μm). The heats of binding were measured as described under “Experimental Procedures.”

FIGURE 3.

Plot of observed enthalpies of binding against buffer ionization enthalpies for the interactions of MMP1c and MMP14c with different N-TIMPs. A, titrations of NT2 (circles), NT1 (squares), and NT1 T98L mutant (triangles) with MMP-4c. B, titrations of NT2 S2D/S4A mutant (circles) and S2D mutant (squares) with MMP1c. Data for the titration of WT NT2 with MMP1c, taken from Wu et al. (6), are represented by the line with no data points. Titrations were generally not repeated because of the large amounts of purified proteins required for each experiment (∼1500 μg of MMP and 700 μg of N-TIMP). However, data from four titrations, conducted in different buffers, were analyzed by linear regression analysis to determine ΔH_int^o and N_H+. Also data from four titrations at different temperatures were similarly analyzed to determine ΔC_p for each MMP/inhibitor pair so that the two key parameters, ΔH_int^o and ΔC_p, for each NTIMP·MMP interaction were derived from four titrations.

Correlation of Thermodynamics with Structure

As discussed previously (5, 6) the ΔC_p^o value for a protein-protein interaction is generally considered to be related to changes in nonpolar and polar-accessible surface area, ΔASA_np and ΔASA_pol (Equations 1 and 2) on complex formation (where surface burial has a negative sign),

The parameterizations of the coefficients for changes in nonpolar and polar surface used here were a = 0.28 ± 0.12 cal mol⁻¹ K⁻¹ Å⁻² and b = −0.09 ± 0.30 cal mol⁻¹ K⁻¹ Å⁻² (36). The enthalpy of binding (ΔH^o) at 60° (35) was calculated using the relationship,

where c is −7.27cal mol⁻¹ Å⁻², and - is 29.16 cal mol⁻¹ Å⁻² (4). ΔH^o at 25 °C is then calculated using the calculated value for ΔC_p. Polar and apolar surface areas in the interfaces of N-TIMP·MMP complexes were measured from atomic coordinates using InterProSurf (37).

Results and Discussion

Effect of the T98L Mutation in NT1 on Its Interactions with MMP3 and MMP14

For the interactions of NT1, NT2, and the T98L mutant of NT1 with MMP14, enthalpies of binding (ΔH_obs) were determined by isothermal titrations at 291 K (Fig. 2) in buffers with different enthalpies of ionization (Pipes, Hepes, Mops, Bes, and Aces). These values were analyzed by linear regression analysis of the plot of ΔH_obs against ΔH_ion using the relationship

where ΔH_ion is the enthalpy of ionization of the buffer, N_H+ is the number of protons taken up (positive values) or released to the buffer during the protein-protein interaction, and ΔH_int^o is the enthalpy change independent of buffer (5, 6). These analyses (Fig. 3A) indicate that there is negligible release of protons for the interactions of WT NT1 and NT2 with MMP14 (N_H+ of +0.06 ± 0.00 and +0.08 ± 0.01, respectively), whereas the interaction with the NT1 T98L mutant releases one proton (N_H+ of 1.02 ± 0.10). The interactions all have highly unfavorable ionization-independent enthalpy changes, ranging from 9 kcal/mol for NT1 to 14.7 kcal/mol for the NT1 T98L mutant (Table 1). Their free energies of binding (ΔG) were calculated from the K_i values determined by inhibition kinetics at 298 using ΔG^o = RTln(1/K_i) (see Table 3). ΔH_obs values from titrations in HEPES buffer at 291, 298, 303, and 310 K (Table 2) were used to determine ΔC_p^o values using the relationship,

TABLE 1.

Enthalpies of binding for the interactions of WT NT1, NT1 T98L, and NT-2 with MMP3c and NT1 T98L with MMP14c in buffers of different enthalpies of ionization

Titrations were carried out at 291 K. ΔH_int, the intrinsic enthalpy change N_H+ and ionization change were calculated by linear regression.

Buffer	ΔHion	ΔHobs
		MMP3c·NT1 T98L	MMP14c·NT2 WT	MMP14c·NT1 WT	MMP14c·NT1 T98L
		kcal/mol
Pipes	2.71	4.65 ± 0.08	10.17 ± 0.10a	11.77 ± 0.37	14.83 ± 0.37
Hepes	4.94	2.63 ± 0.03	10.38 ± 0.09	13.82 ± 0.24	14.96 ± 0.25
Mops	5.20	2.48 ± 0.03
Bes	6.01		10.44 ± 0.11	14.61 ± 0.62	15.04 ± 0.25
Aces	7.55	1.51 ± 0.20	10.51 ± 0.06	16.81 ± 0.30	15.10 ± 0.20
NH+		−0.65 ± 0.11	0.08 ± 0.01	1.02 ± 0.10	0.06 ± 0.003
ΔHint°		6.11 ± 0.62	10.00 ± 0.05	8.87 ± 0.54	14.68 ± 0.02

^a Standard errors for fitting data to a single site model using Origen software.

TABLE 3.

Thermodynamic profiles for interactions of NT1 variants and NT2 with MMP3c and MMP14c, at 298 K

Parameter	MMP3c·NT2 WTa	MMP3c·NT1 WTa	MMP3c·NT1 T98L	MMP14c·NT2 WT	NT1 WT·MMP14c	NT1T98L/ MMP14c
ΔHint (kcal/mol)	5.5 ± 0.2b	6.5 ± 0.3b	6.9 ± 0.6	8.0 ± 0.1	6.1 ± 0.5	10.7 ± 0.02
Ka	2.3 × 108	3.5 × 108	1.6 × 109	1.8 × 1010	3.1 × 106	6.7 × 106
ΔG1M (kcal/mol)	−11.1 ± 0.2	−11.7 ± 0.1	−12.3	−13.7	−8.6	−9.1
TΔSint (kcal/mol)	16.6 ± 0.2	18.2 ± 0.4	19.2 ± 0.6	21.7 ± 0.05	14.7 ± 0.5	19.8 ± 0.0
ΔCpo (cal/mol/K)	−47.2 ± 3.7	−50 ± 6 (−51)c	+130 ± 7 (+139)c	−288 ± 17 (−289)c	−398 ± 11 (−409)c	−575 ± 29 (−576)c
TΔSsolv (kcal/mol)	3.6	3.8	−10.6	23.5 ± 1.4	32.4 ± 0.9	46.8 ± 2.4
Estimated TΔSconf d	16.0	17.4	32.8	1.2 ± 1.4	−14.7	−24.0

^a Data were from Wu et al. (6).

^b Calculated from values at 291K (6).

^c Corrected for buffer ionization dependence (6).

^d Estimated by assuming a cost of 3 kcal/mol for decrease in entropy of translational and rotational degrees of freedom arising from the protein-protein interaction.

TABLE 2.

Enthalpies of binding for the interactions of NT1 T98L with MMP3c and NT1, NT1 T98L, and N-cT2 with MMP14c at different temperatures

ΔC_p was determined by linear regression of ΔH_obs, and K and was used to estimate ΔS_solv at 298K as described under “Results and Discussion.”

Temperature (K)	ΔHobs
	MMP3c·NT1 T98L	MMP14c ·NT2 WT	NT1 WT/· MMP14c	NT1 T98L·MMP14c
	kcal/mol
291	2.63 ± 0.03	10.38 ± 0.09	13.82 ± 0.24	14.96 ± 0.25
298	3.38 ± 0.04	8.69 ± 0.04	10.77 ± 0.09	11.28 ± 0.18
303	4.09 ± 0.08	7.27 ± 0.03	9.04 ± 0.09	8.70 ± 0.10
310	5.09 ± 0.08	4.90 ± 0.02	6.18 ± 0.07	3.96 ± 0.14
ΔCpo (cal/mol/K)	130 ± 7	−288 ± 17 (−289)a	−398 ± 11 (−409)a	−575 ± 29 (−576)a
ΔSsolv (cal/mol)	−33	74	102	148

^a Corrected for buffer ionization dependence (6).

The value of ΔC_p^o is provided by the slope of a plot of ΔH_obs against temperature (Fig. 4A). The ΔG^o values were determined at 298 K, but the ΔH_int values were measured at 291 K. Therefore, to obtain a set of parameters at the same temperature, ΔC_p for the interaction was used to calculate the ΔH_int at 298 K from the value at 291 K (Table 3). TΔS_int values for the mutants were calculated from ΔG and ΔH_int at 298 K (Table 3). These results indicate that the weaker binding of NT1 to MMP14 relative to NT2 reflects a 7 kcal/mol lower TΔS_int of binding. The increased affinity arising from the T98L mutation results from an increase in TΔS_int that is partly offset by an (unfavorable) increase in the ΔH_int of binding (Table 3).

FIGURE 4.

Plot of observed interaction enthalpies of binding against temperature (K) for different N-TIMP interactions with MMPs. A, data for the titration of NT2, NT1, and the T98L mutant of NT1 with MMP14c are displayed as circles, squares, and triangles, respectively. B, results for the titrations the NT2 S2D/S4A mutant (circles), NT2 S2D mutant (squares), and NT2 (no symbols and taken from Wu et al. (6)) with MMP1c. Results for the titration of MMP3c by the NT1 T98L are represented by filled circles. The lines were generated by linear regression analysis.

Further analysis clarified the source of the entropy changes that affect the binding of these N-TIMP variants with MMP14. The overall entropy change, ΔS_int, includes contributions from the interacting proteins (ΔS_protein) and solvent (ΔS_solv), of which the latter can be estimated from the ΔC_p^o for the interaction using the relationship

where Ts* is the reference temperature (385 K) at which the hydrophobic contribution to ΔS is zero (4, 35). ΔS_protein includes negative, unfavorable effects arising from the loss of translational and rotational freedom T(ΔS_trans + ΔS_rot) on complex formation, which has been estimated to be ∼3 (±2.4) kcal/mol for the NT1/MMP3cd interaction (5) and is expected to be similar for other N-TIMP·MMP interactions (6). It also includes the change in conformational entropy, ΔS_conf, that encompasses an unfavorable loss of entropy resulting from increased rigidity of the interaction sites of the two proteins in their complex. However, it may also contain favorable entropy increases resulting from increased dynamics in regions distant from the interaction sites in the bound protein populations (5, 6). ΔC_p^o values for the interactions with MMP-14 are large and negative and lead to estimates of 32–47 kcal/mol for increases in TΔS_solv for the interactions with NT1, NT2, and NT1 T98L (Table 3). Using these values we estimate that the binding of either NT1 or NT1 T98L to MMP-14c results in energetic costs reflecting conformational entropy changes (TΔS_conf) of −14.7 and −24.0 kcal/mol for NT1 and NT1 T98L, respectively (Table 3). The interaction with NT2 is associated with an insignificant change in TΔS_conf (1.2 ± 1.4 kcal/mol). These results show that the weak binding of NT1 to MMP-14c arises from a large conformational entropy penalty. Surprisingly, the T98L mutation increases this penalty, but this increase is exceeded by the enhanced hydrophobic effect (TΔS_solv), consistent with the hydrophilic to hydrophobic T98L substitution in the NT1 reactive site.

The T98L mutation in NT1 also increases the affinity for MMP-3 by a factor of 4 (15), but the thermodynamic origins of this are different. A more unfavorable ΔH_int (8.2 versus 6.0 kcal/mol) is exceeded by an increase in TΔS_int (Table 3). Unexpectedly, ΔH_obs for binding to MMP3c increases with temperature (Fig. 4B), indicating a positive ΔC_p value of 124 cal/mol/K. From this we estimate a value of −10.6 kcal/mol for TΔS_solv, an unfavorable contribution to ΔG that is compensated by an estimated increase in TΔS_conf of 33 kcal/mol. In contrast, the interaction of MMP3c with WT NT1, characterized previously, has a ΔC_p of −50, a favorable TΔS_solv of 3.8 kcal/mol, and a smaller TΔS_conf of 17.4 kcal/mol (5).

Interaction of the NT2 S2D and S2DS4A Mutants with MMP-1c

The interactions of these two mutants were characterized with only MMP1c because they do not inhibit MMP3c or MMP14c (18). Linear regression analysis of ΔH_obs values for isothermal titrations at 291 K in buffers with different enthalpies of ionization (Table 4; Figs. 3 and 5) indicates fractional release and uptake of protons, (N_H+) of −0.47 and +0.46, respectively, for the S2D and S2D/S4A mutants compared with a negligible uptake of +0.14 previously determined for WT NT2. This analysis also shows that the ionization-independent ΔH_int for the single site mutant, S2D, is 9.5 kcal/mol, much more unfavorable than that for the double mutant, S2D/S4A (1.5 kcal/mol; Table 4), contributing to the weaker binding of S2D shown by ΔG values (calculated from the K_i values) of −10.2 kcal/mol for S2D and −14.5 kcal/mol for S2D/S4A (see Table 6). As previously discussed, ΔH_obs values from titrations at different temperatures (Table 5, Fig. 4B) were used to determine ΔC_p^o. This in turn was used to calculate the ΔH_int at 298 K and to estimate ΔS_solv. Values of TΔS_int for both mutants, calculated from ΔG and ΔH_int values at 298 K, show that the entropy contribution for S2D is ∼2 kcal/mol greater than for the S2D/S4A mutant. The thermodynamic parameters of S2D/S4A are similar to those for WT NT2, but the weaker binding of the S2D mutant reflects a larger enthalpy penalty that is only partly compensated by the increase in TΔS_int (Table 6).

TABLE 4.

Enthalpies of binding for the interactions of variants of NT2 with MMP1c in buffers of different enthalpies of ionization at 291 K

Titrations were carried out at 291 K. ΔH_int, the intrinsic enthalpy change N_H+ and ionization change were calculated by linear regression analysis.

Buffer	ΔHion	ΔHobs
		NT2a	NT2 S2D/S4A	NT2 S2D
			kcal/mol
Pipes	2.71		2.83 ± 0.02	8.26 ± 0.11
Hepes	4.94		3.82 ± 0.03	7.36 ± 0.10
Bes	6.01		4.21 ± 0.04	6.53 ± 0.08
Aces	7.55		5.06 ± 0.04	6.09 ± 0.12
NH+		0.14	0.46 ± 0.03b	−0.47 ± 0.05
ΔHint° (kcal/mol)		2.54	1.54 ± 0.17	9.53 ± 0.28

^a Data are from Ref.6.

^b S.E. for fitting data to Equation 3.

FIGURE 5.

Isothermal calorimetric titration of NT2 S2D/S4A mutant with MMP1c in different buffers at 291K. Left, aliquots (20 μl) of MMP1c (150 μm) were injected into NT2 (30 μm) in ACES buffer, pH 7.4. Right, aliquots (20 μl) of MMP1c (150 μm) were injected into NT2 (30 μm) in HEPES buffer, pH 7.4. The heats of binding were measured as described under “Experimental Procedures.”

TABLE 6.

Thermodynamic profiles for interactions of NT2 variants and NT1 with MMP1c, at 298 K

Parameter	NT2 WTa	NT2 S2D/S4A	NT2 S2D	NT1 WTa
ΔHint (kcal/mol)	0.58	0.79 ± 0.2b	8.3 ± 0.3b	−0.86
Ka	2.8 × 1010	4 × 1010	2.9 × 107	4.3 × 109
ΔG1M (kcal/mol)	−14.2	−14.5	−10.2	−13.4
TΔSint (kcal/mol)	14.8	16.2 ± 0.2	18.5 ± 0.3	12.5
ΔCpo (cal/mol/ K)	−278 ± 10	−102 ± 25 (−107)c	−165 ± 25 (−160)b	−189
Estimated TΔSsolvc (kcal/mol)	21.2	8.2 ± 1.9	12.2 ± 1.8	14.8
Estimated TΔSconfd	−3.4	11.0	9.3	0.7

^a Values were taken from Wu et al. (6).

^b Values calculated at 298 K using ΔC_p.

^c Corrected for buffer ionization dependence (6).

^d Estimated by assuming a cost of 3 kcal/mol for decrease in entropy of translational and rotational degrees of freedom arising from the protein-protein interaction.

TABLE 5.

Enthalpies of interaction of NT2 variants with MMP1c at different temperatures

ΔC_p was determined by as described in the legend to Table 3.

Temperature (K)	ΔHobs
	NT2a	NT2 S2D/S4A	NT2 S2D
		kcal/mol	kcal/mol
291		3.82 ± 0.03	7.36 ± 0.10
298		2.94 ± 0.04	5.57 ± 0.09
303		2.40 ± 0.04	5.01 ± 0.09
310		1.88 ± 0.03	4.15 ± 0.16
ΔCpo (cal/mol/K)	−278	−102 ± 25 (107)b	−165 ± 25
ΔSsolv (cal/mol)	71	27	42

^a Data were from Ref.6.

^b Corrected for buffer ionization dependence (6).

The source of the entropy driving the interactions WT NT2 and the mutants with MMP1c was determined as described in the previous section using solvent entropy changes (ΔS_solv) estimated from the heat capacity changes for the interactions. The values of TΔS_conf at 298 K indicate that conformational entropy increases contribute −9.3 and −11.0 kcal/mol to ΔG for interactions of S2D and S2DS4A with MMP1c, contrasting with WT NT2, which has an unfavorable TΔS_conf of −3.4 kcal/mol, presumably derived from increased rigidity in the interaction interface. The thermodynamic parameters previously determined for the interaction of NT1 with MMP1c are also given in Table 6.

Relationship of Thermodynamic Profiles to Structures

Like previously studied N-TIMP·MMP interactions (5, 6) the present interactions have minimal to strongly positive ΔH_int values and are driven by large entropy increases. This helps to explain how TIMPs inhibit numerous matrixins whose active sites are adapted to binding diverse biological targets.

Crystallographic structures relevant to the interactions with MMP14 are the TIMP2·MMP14c complex, pdb 1BUV, and the complex of the V4A/P6V/T98L of NT1 with MMP14c, pdb 3MA2 (24, 26). A model of the T98L NT1 mutant with MMP3c was generated from pdb 1UEA (23) by truncating residues 126–180, changing Thr-98 to Leu followed by energy minimization. The V4A, P6V, and T98L mutations in NT1 individually lower the K_i for MMP14c 2–3 fold, suggesting that they contribute additively to the ∼10-fold increase in affinity of the triple mutant (14) without a major conformational change, supporting the use of the 3MA2 structure (26) as a template. The areas of apolar and polar surface in the interfaces of the models were analyzed to predict the values of ΔC_p and ΔH (at 25 °C) for the interaction (27, 28) for comparison with those determined experimentally (Table 7). These values show reasonable agreement for the MMP14c complexes, but the experimentally determined ΔC_p values for the MMP3c complexes stand out as being far less negative than those calculated from the structures.

TABLE 7.

Comparison of the ΔC_p and ΔH_int (298 K) values calculated from the polar and apolar interface surface areas of NTIMP·MMP complexes, as described under “Experimental Procedures,” with those determined experimentally

Complex	Parameters
	Buried surface areas		ΔCp		ΔH
	Polar	Apolar	Calculated	Experimental	Calculated	Experimental
	Å2		cal/mol/K		kcal/mol
MMP1·NT1	564	971	−221	−194	−0.9	+0.5
MMP3·NT1	514	1525	−381	−51	+9.4	+6.5
MMP3·NTI T98L	558	1532	−388	+139	+10.1	+6.9
MMP14·NT1	512	1205	−292	−398	+4.1	+6.1
MMP14·NT1 T98L	505	1218	−296	−575	+4.5	+10.7
MMP14·NT2	659	1661	−391	−289	+3.9	+8.0

We previously developed models of complexes of NT2 and its S2DS4A mutant with MMP1c (18). These suggested that the double mutation results in more extensive contacts of NT2 Asp-2 with the S1′ pocket of MMP1c relative to Ser2 in WT NT2 (18). The selective inhibition of MMP1c by the S2D/S4A and S2D mutants appears to result from the unique presence of R114 in MMP1c (see Fig. 1), which is replaced by uncharged residues in other human MMPs except for MMP21 (Lys) and MMP23 (His). In contrast, the model of the complex of the NT2 S2D/S4A mutant with MMP-3c shows increased separation in the S1′ pocket, suggesting that charge repulsion between Asp-2 of the inhibitor and the catalytic site Glu-202 of MMP-3c is responsible for the extremely weak binding (18). In the complex of the S2D/S4A mutant with MMP1c, favorable electrostatic interactions between Asp-2 of the NT2 mutant and Arg214 in MMP-1 allows high affinity binding. The greater polarity of Asp as compared with S2 of WT NT2 also results in less negative ΔC_p values for the interactions of this mutant with MMP1. This leads to lower (estimated) TΔS_solv values and increased values for TΔS_conf implying that the reduced hydrophobic effect is compensated by enhanced conformational dynamics. We propose that structural adjustments in the interaction interface resulting from the insertion of the negatively charged Asp-2 are transmitted through the protein structures to more distant sites, reducing stability and increasing conformational dynamics (5).

Conformational Dynamics and Selectivity in MMP Inhibition

The disagreement between the experimental and calculated values for ΔC_p for the NT1/MMP3c interaction was previously attributed to large conformational differences the structures of the both proteins in their free and bound states (19, 22, 23). As a result, the areas of polar and apolar surface quantified from the interaction interface in the complex differ from those buried during the interaction process (5, 6). In contrast, in the NT1·MMP1c complex, the structure of MMP1c shows only minor differences when compared with the structure of the MMP1c (11). These analyses are misleading because they treat the crystallographic structures as static models, whereas they are the average structures of assemblies of conformers (38, 39). The process of complex formation results in the selection of populations of conformers that differ from those in the free state; the selected populations differ in conformational dynamics, solvent interactions, and structure. Fig. 6 compares the structures of the NT1 components from the crystallographic structures of various MMP complexes and with two chains from the solution NMR structure of free NT1 (11, 22, 23, 26, 27) showing large differences, particularly in the loops between β-strands A and B and B and C where missing electron density indicates local unfolding. This may expose apolar groups, making a positive contribution to ΔC_p. The core of the reactive site, including the N-terminal five residues is similar in the different complexes but differs from the NMR structure of the free protein (Fig. 6).

FIGURE 6.

Superimposed ribbon structures of NT1 extracted from crystallographic structures of different complexes and solution NMR structures of the free protein. The structures from the complexes are colored as follows: pink, MMP1c (PDB code 2jot); cyan, MMP3c (PDB code 1uea); blue, MMP14c (PDB code 3ma2); purple, MMP10c (PDB code 3v96). The free NT1 structures were chains 1, 20 and 29 from PDB code 1d2b and are colored light gray. The structures were superimposed and displayed using CHIMERA (43).

Eftink et al. (40) have shown that if an interacting protein has two conformational states that both interact with a binding partner, indicating non-mandatory coupling between binding and conformational change, ΔC_p can have positive or negative values depending on parameters relating to the conformational transition (40). This may explain the “anomalous” ΔC_p values for N-TIMP interactions with MMP3c, including the positive ΔC_p for the interaction of MMP3c with the NT1 T98L mutant.

Previously reported dynamics simulations with NT1 and its T98L mutant suggested that the mutation reduced the flexibility of its interface for MMP-14, including the highly flexible N-terminal region, leading to a reduced ΔS_conf penalty for binding (26). Our experimental data indicate that WT NT1 binding carries a large entropic penalty that reduces TΔS_conf by 12 kcal/mol. The NT1 T98L mutation increases this penalty by 8 kcal/mol, and the increased K_a comes from an increase in solvent entropy (TΔS_solv), estimated from the more negative ΔC_p. The reduced flexibility in free NT1 indicated by dynamics simulations appears to be negated by a greater loss of conformational entropy in the NT1·MMP14 complex that may arise from additional interactions between Leu-98 of the NTIMP and the MMPs that are not present in the complex with WT NT1. Such interactions lead to a more negative ΔC_p, reflecting an increase in the hydrophobic effect.

Fig. 7A shows the strong negative correlation between ΔS_solv (derived from ΔC_p) and ΔS_conf for all currently characterized N-TIMP·MMP interactions (adjusted R² = 0.975). The combined data for the interactions of three MMPs with WT and mutant forms of NT1 and NT2 do not include all possible mutant N-TIMP·MMP combinations. However, the data for the interactions of the WT N-TIMPs with the three MMPs show a similar correlation between ΔS_conf andΔS_solv. One explanation of ΔS_solv/ΔS_conf compensation is that ΔS_conf is calculated from ΔS_solv and ΔS_int; TΔS_int for the 10 currently characterized interactions has a low variance (57.7 ± 9.4 cal/mol) so that the apparent compensation between ΔS_solv and ΔS_conf is not unexpected. In Fig. 7A, the data points for interactions with each MMP are grouped together, and the graphical summary of thermodynamic parameters in Fig. 7B shows that interactions involving MMP3 have the highest ΔS_conf and lowest ΔS_solv values, whereas those involving MMP14 have the lowest (mostly negative) ΔS_conf and highest ΔS_solv. Interactions between NTIMPs and MMP1 have intermediate values of ΔS_conf and ΔS_solv and the least unfavorable ΔH_int. This is consistent with our previous observation, based on less data, that the character of the MMP has a major influence on the proportions of ΔS_conf and ΔS_solv (6), apparently reflecting intrinsic differences in structure and flexibility between the MMPs. Interactions with MMP14 bury more nonpolar surface than those with MMP1, resulting in a more positive ΔS_solv. MMP3c has a higher conformational flexibility than MMP1c and MMP14c (41), reflected in conformational changes in complexes with inhibitors and TIMP-1 (23, 42). Possibly, these differences between MMPs might be exploited in designing more selective TIMP mutants or other inhibitors, but this could be limited by the observed compensation between ΔS_conf and ΔS_solv.

FIGURE 7.

Contributions of ΔH_int, ΔS_solv, and ΔS_conf to N-TIMP·MMP interactions. A, bar chart of values for different interactions. Black, ΔH_int; white, ΔS_solv; gray, ΔS_conf. B, linear inverse relationship between ΔS_solv and ΔS_conf for all characterized interactions. Data for interactions with MMP1c are denoted by circles, MMP3c by squares, and MMP14c by triangles; WT N-TIMPs are represented by open symbols and engineered N-TIMPs by filled symbols. The units of ΔS are cal/mol. The line, generated by regression analysis, represents the relationship: ΔS_conf = 67.6 − ΔS_solv.

Conclusions

Specific protein-protein interactions are pivotal for the control of numerous biological processes including those mediated by regulated proteolysis. Although the four human TIMPs are high affinity metalloproteinase inhibitors, they show little selectivity in their interactions with the 23 human MMPs. This is consistent with entropy-driven binding, which encompasses free energy contributions from the relatively nonspecific hydrophobic effect (solvent entropy changes) and/or changes in conformational entropy. The mutually compensating ΔS_solv and ΔS_conf, estimated using the key thermodynamic parameter, ΔC_p (44), are important in modulating NTIMP·MMP interactions. The character of the MMP strongly affects their proportions, and the magnitude of ΔH_int (Fig. 7B). This is illustrated by the T98L mutation in NT1, which enhances binding to MMP-3 by increasing ΔS_conf and to MMP-14 by enhancing ΔS_solv. The highly conserved N-terminal regions of TIMPs have a high level of flexibility in the free protein (22), a common feature of multi-specific protein interaction sites (45). Mutations in the N terminus have major effects on avidity and selectivity for MMPs. In previous studies, NTIMP mutants identified as having the greatest selectivity against MMP-1 are the NT1 T2R (14) and T2R/V4I mutants (16), whereas that with the greatest selectivity for MMP-1 is the NT2 S2D/S4A mutant (18). These mutations alter electrostatic interactions between the NTIMP and the unique Arg-214 in the MMP S1′ site, suggesting that the N-terminal region of TIMPs and unique active site features of MMPs are both keys to developing selective inhibitors.

Author Contributions

K. B. devised and supervised the study and wrote the paper. H. Z. and Y. W. designed and performed the experiments and analyzed the data.