A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate 5E ground state with strong in-state spin–orbit coupling (SOC). We study the competing effects of SOC and the 5E⊗ε multimode Jahn–Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d6 configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpaR)]− (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4.
The prototypical proprotein convertase furin proteolytically activates many precursor proteins and is essential for cellular homeostasis of the cell. Furin and other proprotein convertase are also associated with a number of diseases, including cancer, atherosclerosis, hypercholesterolaemia, and infectious diseases. A hallmark of furin and its physiologic function is its stringent specificity for polybasic substrates. Here we describe several structural states of the protein by X-ray crystallography and further characterize them by molecular dynamics simulations. The transition between these conformers is triggered by substrate binding and calcium ligation, respectively, and helps explain the stringent specificity of furin and its functional features. These studies may pave the way for novel strategies of structure-guided inhibitor development.
Proprotein convertases (PCs) are highly specific proteases required for the proteolytic modification of many secreted proteins. An unbalanced activity of these enzymes is connected to pathologies like cancer, atherosclerosis, hypercholesterolaemia, and infectious diseases. Novel protein crystallographic structures of the prototypical PC family member furin in different functional states were determined to 1.8–2.0 Å. These, together with biochemical data and modeling by molecular dynamics calculations, suggest essential elements underlying its unusually high substrate specificity. Furin shows a complex activation mechanism and exists in at least four defined states: (i) the “off state,” incompatible with substrate binding as seen in the unliganded enzyme; (ii) the active “on state” seen in inhibitor-bound furin; and the respective (iii) calcium-free and (iv) calcium-bound forms. The transition from the off to the on state is triggered by ligand binding at subsites S1 to S4 and appears to underlie the preferential recognition of the four-residue sequence motif of furin. The molecular dynamics simulations of the four structural states reflect the experimental observations in general and provide approximations of the respective stabilities. Ligation by calcium at the PC-specific binding site II influences the active-site geometry and determines the rotamer state of the oxyanion hole-forming Asn295, and thus adds a second level of the activity modulation of furin. The described crystal forms and the observations of different defined functional states may foster the development of new tools and strategies for pharmacological intervention targeting furin.
Furin belongs to the family of highly specific, calcium-dependent proprotein/prohormone convertases (PCs) (1), endoproteinases that feature a catalytic domain of homology to subtilisin and activate a large number of secreted proteins by limited proteolysis. Furin is a type I transmembrane serine-protease that is ubiquitously expressed and cycles from the trans-Golgi network to the cell membrane, as well as through the endosomal system. In mammals, the PC family embraces seven members that cleave after multiple basic residues (furin, PC1, PC2, PC4, PACE4, PC5/6, and PC7) and at the general cleavage site (R/K)Xn(R/K)↓ (where “↓” represents the scissile peptide bond), with furin preferentially recognizing the motif R-X-K/R-R↓ (2). This highly sequence-specific cleavage is essential for the activation of numerous PC substrates (2). The PCs are also involved in a large number of pathologies, including bacterial and viral infections, as well as cancer and metastasis. Therefore, these enzymes are intensely investigated as drug targets (3), using for example, peptide-derived compounds (4⇓⇓⇓⇓–9), nonpeptidic small molecule compounds (10, 11), and protein-based inhibitors (12⇓⇓–15).
Different crystal structures of the inhibitor-bound murine (16) and human (6, 17) enzyme, together with structural studies of the yeast homolog Kex2p (18, 19) and modeling approaches (9, 20), gave hints of how substrates and substrate-derived inhibitors bind with high specificity to furin and to the PCs, but suffer from the lack of structural information of the unliganded enzyme. The commonly accepted notion is that the PCs bind their cognate substrates via recognition at several subsites, typically involving multiple tight contacts and hydrogen bonds. Catalytic efficiency, however, in addition to strong and fast binding of substrate, requires rapid chemical transformation and fast release of product.
The chemical reaction catalyzed by furin and other proteases—the hydrolysis of the scissile peptide bond—often involves limited structural changes of the active site residues, which are unlikely to perturb remote substrate-binding subsites of the enzyme. Furin has an extended substrate-binding area where typically all specificity-determining residues are located N-terminal to the scissile peptide bond, suggesting that the C-terminal segment is more loosely bound and may dissociate readily after hydrolysis. Potent noncovalent inhibitors are characterized by very slow off-rates, a feature that may apply to very tight binding substrates that are poorly cleaved as well, and can thus act as efficient inhibitors as those, for example, shown in other protease families for the slowly hydrolyzed dipeptidyl peptidase IV substrate diprotin A (21).
The high substrate selectivity and enzymatic activity of furin, and its strict Ca2+ dependence, demand a structure-based explanation. Although Ca2+ is not involved in the catalytic cycle per se, all PCs require calcium for their enzymatic activity (17, 22, 23).
One more distinctive feature of furin in the protease family is its very limited reactivity toward typical covalent inhibitors of serine proteases, like diisopropylfluorphosphat (DFP) and phenylmethylsulfonylfluorid (PMSF). Interestingly, the spatial restrictions at and around the catalytic serine residue 368 of furin are structurally reminiscent of typical trypsin-like proteases. This similarity is especially evident for the deep S1 pocket selecting for basic amino acid side chains at P1, the β-strand of the enzyme (Ser253-Gly255 in furin vs. Ser214-Gly216 in trypsin), displaying antiparallel β-sheet–like contacts with a peptidic substrate and a typical hydrophobic tryptophane (Trp254 in furin vs. Trp215 in trypsin) in its center. Therefore, one would expect a similar reactivity of furin against nonselective, covalent inhibitors that do not specifically interact with the different specificity pockets, but probe the nucleophilic catalytic site serine residue; however, this has not been observed. Furin is also completely inert against typical monobasic trypsin-substrates (our own observations and those, for example, in refs. 22 and 24). This is observed even though (i) the P1 requirements of the two enzymes are comparable, (ii) furin accepts different residues at its S2-pocket, and (iii) its S3-pocket is not very specific.
To address the above questions and to find out how the high negative-charge density within the active site cleft of furin is stabilized in its ligand-free state, we have studied the structure of the unliganded enzyme as well as of different Ca2+ and inhibitor-bound forms by X-ray crystallography at high resolution. Comparison of the different crystal structures together with solution studies and molecular dynamics (MD) simulations give hints of the enzymatic mechanism and the unique features of this central regulatory endoproteinase.
Inhibitor-Induced Structural Changes of the Active-Site Cleft.
Human furin was crystallized in its unliganded state, its structure solved by molecular replacement (MR), and refined up to 1.8-Å resolution at high quality (Fig. 1A and Table S1). Structure alignments of unliganded furin with the inhibitor-bound human and mouse furin structures demonstrated high overall similarity (Cα-rmsd of 0.22 Å and 0.28 Å, respectively). A close inspection of the active-site residues and the substrate-binding cleft, however, revealed substantial differences.
Analysis of substrate induced structural rearrangements of furin. (A) Overall structure of human unliganded furin (catalytic and the P-domains are in gold and blue, respectively). The catalytic residues (cyan stick model), the substrate binding pockets (labeled S1–S5), and bound ions (purple sphere, Na+; green spheres, Ca2+) are indicated. (B) The Cα-displacement values (intervals <0.3 Å, 0.3–0.8 Å, and >0.8 Å are highlighted in cyan, yellow, and magenta, respectively) were mapped to the molecular surface.
To directly investigate structural changes occurring upon substrate binding in identical crystal forms, we soaked the unliganded crystals with the substrate analogous, noncovalent inhibitor m-guanidinomethyl-phenylacetyl-Arg-Val-Arg-(4-amidomethyl)-benzamidine (MI-52, #26 in ref. 4). The active-site cleft of furin is oriented toward large solvent channels in these crystals, enabling the binding of large peptidic compounds to the protease unperturbed by crystal packing. The crystal structure was refined at a resolution of 2.0 Å (Table S1). A residue-wise comparison of unliganded and inhibitor-bound forms revealed a number of significant structural changes (Fig. S1A). Hotspots of conformational changes include the catalytic residues His194, Ser368, Asn295 of the oxyanion hole, the sodium binding site (Thr309 and Ser316), and residues in direct contact with the inhibitor peptide (e.g., the region Ser253–Pro256, the alignment template). Mapping of the Cα displacement to the surface of the structure induced by inhibitor binding revealed a concerted local rearrangement at the substrate-binding cleft (Fig. 1B and Fig. S1B). These displacements propagate with diminishing amplitude to the core of the protease (Fig. S1C). The catalytic residues and the alignment template are well defined in the electron-density maps (Fig. S2 A and B) and characterized by low flexibility.
Structural analysis of furin in its unliganded vs. its MI-52–bound states. (A) Plot of the Cα-displacement values of the Cα atoms covering all amino acids of furin (intervals <0.3 Å, 0.3–0.8 Å, and >0.8 Å are highlighted in cyan, yellow, and magenta, respectively). (B) Mapping of the respective values to the molecular surface and colored according to A. (C) Cartoon representation colored according to A. Bound ions are shown as light gray (Na+) and dark gray (Ca2+) spheres.
Electron-density maps observed for the active-site residues and the alignment template of human furin. Stereo panels show the structures in stick representation. The 2Fo–Fc simulated annealing composite-omit electron density maps are given as blue-colored mesh, which is contoured at 1.0 σ. (A) Unliganded furin. (B) Furin complexed with MI-52. (C) Unliganded furin in presence of EDTA. (D) Furin in presence of EDTA and complexed with MI-52.
A structural comparison of the substrate-binding region indeed revealed two distinct conformational states for furin (Fig. 2A and Fig. S3A). In contrast, the homologous unspecific protease subtilisin showed a high overall structural similarity (Cα rmsd of 0.24 Å) of the unliganded structure [PDB ID code 3UNX (25)] and the subtilisin–eglin-c complex [PDB ID code 1CSE (26)] as well as identical conformations of the active site cleft (Fig. 2B and Fig. S3B).
Structural comparison of substrates binding to the active sites of furin and to subtilisin Carlsberg. (A) Structural alignment of selected residues of unliganded furin (yellow carbons) and inhibitor-bound furin (gray carbons; inhibitor: ball-and-stick). Steric clashes between bound inhibitor/substrate and unliganded furin are highlighted as red line patterns. (B) Structural alignment of unliganded subtilisin (orange carbons) and inhibitor-bound subtilisin (green carbons). (C) Structural alignment of inhibitor-bound subtilisin (green carbons) and furin (gray-colored stick model). Important interactions are always highlighted by dashes.
Stereo representation of the structural comparison of substrate binding by furin and subtilisin Carlsberg. Detailed view of the alignment template and the active-site residues of inhibitor-bound furin (protein: gray-colored stick model; inhibitor: gray-colored ball-and-stick model), unliganded furin (yellow-colored stick model), unliganded subtilisin (light orange-colored stick model), and eglin-c (shown P5–P1 segment Ser-Pro-Val-Thr-Leu) bound subtilisin (protein: light green-colored stick model; inhibitor: dark green-colored ball-and-stick model). (A) Structural alignment of selected residues of unliganded furin and inhibitor-bound furin. Steric clashes between bound inhibitor/substrate and unliganded furin are highlighted as red line patterns around the respective atoms. (B) Structural alignment of unliganded subtilisin and inhibitor-bound subtilisin. Important interactions of the active-site residues and between the alignment template and the inhibitor are highlighted as gray and yellow dashes, respectively. (C) Structural alignment of inhibitor-bound subtilisin and furin. Important homologous amino acids of the proteases are labeled in green (subtilisin) and gray (furin).
A principal component analysis (PCA) was carried out to gain further insight into the structural modifications induced by inhibitor binding and their relationship with furin’s homologous proteins. To allow a direct comparison between furin and the closely related protease subtilisin Carlsberg, a common core of 191 residues was selected to perform the PCA on their Cα atoms. Projecting the crystallographic structures on the first principal component, which captures more than 80% of the variance, shows a clear separation among the furin structures with and without ligand-bound conformations (Fig. 3A), but not among the subtilisin Carlsberg structures, where both unliganded and inhibitor-bound conformations exhibit closer similarity to the furin inhibitor-bound structures. These observations prompted us to consider the first principal component as an appropriate metric to monitor the unliganded and inhibitor-bound states. A detailed inspection revealed that the conformation of residues proximal to the alignment template and the active site of subtilisin and furin are similar in the ligand-bound state (overall Cα rmsd of 0.38 Å) (Fig. 2C and Fig. S3C): specifically, the rotamers of Ser221 of subtilisin and Ser368 of furin, respectively. Conversely, the unliganded conformations of both enzymes differ and reflect the structural transition in furin absent in subtilisin. Interestingly, the PCA covariance matrix unveils a concerted movement between the alignment template (Ser253–Pro256), residues neighboring the sodium binding site (314–317), and the oxyanion hole (290–297 and 365–369) again.
PCA. (A) Projections of furin (squares) and subtilisin Carlsberg (triangles) on the first two principal components. Only human furin structures (green) were used to compute the covariance matrix. Murine furin structures (blue) are shown for comparison only. Open and closed markers represent unliganded and inhibitor-bound structures, respectively. (Inset) The proportion of the structural variation encoded within each principal component. (B) Histograms of MD-simulation frames projected on the first principal component for each simulated system: furin unliganded state (red), furin inhibitor-bound (blue), furin inhibitor-removed (green), subtilisin unliganded state (black), substilisin inhibitor-bound (cyan), and subsitilisn inhibitor-removed (magenta). Projections of the crystallographic structures are shown on the x axis as in A. (Inset) Examples of MD trajectories.
The unliganded structure of furin has the side chain of Ser368 rotated 180° away from the S1 pocket and the scissile peptide bond, as defined in the dec–RVKR–cmk complex structure (16), altering the interaction geometry of the catalytic triad and disrupting the essential hydrogen bond to His194. However, a nucleophilic attack at the scissile peptide bond requires a conformation, as observed in the inhibitor-bound structure. The rotamer of Ser368 as observed in the unliganded structure can thus not enable substrate processing. Interestingly, the rotameric state of Asn295 in the unliganded and the ligand-bound forms is largely identical as long as the Ca2+-(II) site is occupied (see Calcium-Dependent Activity Regulation of Furin, below).
The loss of the hydrogen bond between Ser253-OH and the carbonyl-O of Ser368 appears to facilitate the reorientation of Ser368 in unliganded furin (Fig. 2A and Fig. S3A). In addition, binding of peptide chains to the active-site cleft of furin requires a specific orientation of the alignment template, enabling characteristic backbone interactions and a P1–side-chain recognition. These interactions are incompatible with the unliganded structure (Fig. 2A and Fig. S3A). Furthermore, steric clashes between ligand and the enzyme would occur, especially at P1 and P4. In conclusion, the catalytic residues and the substrate-binding region adopt an inactive conformation in the unliganded furin structure, representing an “off” state. By binding of the substrate-analog inhibitor MI-52, the enzyme switches to a catalytically active “on” state.
Data collection and refinement
MD Calculations Show Switching Between the On and Off States.
Next we assessed the stability of the unliganded and inhibitor-bound conformations by performing MD simulations. For this purpose, furin and subtilisin were simulated in three different conditions: (i) an unliganded state, (ii) an inhibitor-bound state, and (iii) an inhibitor-removed state (protein in its inhibitor-bound conformation with the inhibitor molecule deleted). Histograms collected from projecting MD trajectories on the first principal component show that for furin, the inhibitor-removed state drifts away from its initial inhibitor-bound conformation. It relaxes toward a conformation that resembles the crystallographic unliganded conformation and approaches the relaxation state reached by simulations of furin’s unliganded state (Fig. 3B). In contrast the inhibitor-bound simulations show that the furin–MI-52 complex is highly stable, sampling conformations around its crystallographic pose. Notably, furin simulations in its unliganded state eventually visit the ligand-bound conformation, thereby suggesting that the latter is a thermally accessible state. In subtilisin, all three systems retain their crystallographic conformations and sample inhibitor-bound–like structures (Figs. 2B and 3B and Fig. S3B). These results suggest that in furin, but not in subtilisin, a fraction of the ligand binding energy is spent in transforming the enzyme from an off state to an on state.
Prompted by these observations, we reanalyzed the melting temperatures (Tm) of furin–inhibitor complexes and their dependence on the Ki-values (6). In a semi-logarithmic representation of the data, an apparent linear relationship between pKi (range 6.4–11.3) and Tm can be found. Interestingly, by extrapolation to pKi-values < 6, Tm falls below the value observed for unliganded furin. We reason that the dependence of melting temperature and stability on ligand affinity rests on two opposing factors: a gain in bonding interactions and energy with increasing affinity and a loss by the conformational switch with all ligands, such that the latter prevails with weakly binding ligands.
Specific Entities Define the Structural Difference Between the Two Conformational States.
Comparisons of the unliganded and inhibitor-bound crystallographic structures provide insight regarding to the key structural features that characterize the on state. Different alignment template configurations allow hydrogen bond formation between Ser253γOH and the carbonyl oxygen of Ser368 in the on state, whereas this interaction is absent in the off state. This interaction prompts a Ser368 side-chain rotation of 180° away from the S1 pocket, thereby altering the interaction geometry of the catalytic triad. The MD simulations support this mechanism because, in the furin–inhibitor complex, the Ser253γOH–Ser368O hydrogen bond is observed 88% of the time, considering all repetitions (SI Materials and Methods), as a part of a dynamic process, and the rotameric state of Ser368 is stable in the experimentally observed conformation (Fig. S4A). In contrast, in the furin unliganded system this hydrogen bond is practically never observed (1% of the time) and the distribution of Ser368 χ-angle is bimodal, suggesting a dynamic equilibrium between the two orientations. Interestingly, the dynamic behavior of Thr367 appears to be also related to the on and off states. The Thr367 χ1 dihedral angle (Fig. S4B) displays a single orientation in the liganded state corresponding to the crystal structure, whereas the unliganded form shows, as for Ser368, two stable orientations. However, only one of these orientations corresponds to that observed in the crystals. The MD data suggest that Thr367 χ1 also samples an orientation where its hydroxyl group approaches the S1 pocket and the Asn295’s side chain.
Rotameric states from MD simulations. Histograms are computed from five independent runs of each simulated system: unliganded furin (red), furin with inhibitor MI-52 (blue), unliganded furin in the presence of EDTA (green), unliganded furin with Thr367’s χ1 initially set at 60° (black), unliganded furin in the presence of EDTA and with Asp258 protonated (yellow). For residues Ser368 (A), Thr367 (B), Asp258 (C), and Asn295 (D) the measured quantity is the χ1 dihedral-angle, whereas for Gly255 (E) it is the ψ dihedral-angle. The information is split into two panels for clarity. The Upper panel contains plots from the simulations of unliganded furin, furin with inhibitor, and unliganded furin in the presence of EDTA structures; the Lower panel contains plots corresponding to simulations of unliganded furin with Thr367's χ1 initially set at 60° and unliganded furin in the presence of EDTA with Asp258 protonated. Each curve represents an average histogram (solid lines) with 1 SD as upper limit (error bar). The averages were computed from five independent runs. The values in each inset correspond to the values found in the crystallographic structures.
Conformational changes are also transduced to the single sodium binding site of the protease (Fig. S5). In the unliganded structure the sodium ion is coordinated by the carbonyl oxygens of Thr309, Ser311, and Thr314, the hydroxyls of Thr314 and Ser316, as well as one water molecule, in the preferred octahedral coordination. Upon inhibitor binding, the coordination changes to a tetragonal-pyramidal geometry that is less frequently observed. The side-chain rotations of Ser316 and Thr309 result in breakage of the coordinative bond to the sodium ion and loss of the hydrogen bond between these residues, indicating a switch from a lower (unliganded form) to a higher (liganded form) energy state. Accordingly, in the MD simulations of the unliganded system the rotameric state of Ser316 is highly stable and the Ser316γOH–Thr309γOH interaction is relatively well conserved, being present 50% time in a dynamic fashion considering all repetitions.
Substrate-induced conformational changes of the sodium site in furin. Stereo panels show a superposition of selected residues of unliganded furin (yellow, protein: stick model; nonbonded atoms: spheres) and inhibitor-bound furin (gray, protein: stick model; inhibitor: ball-and-stick; nonbonded atoms: spheres). (A) Superposition of the unliganded inhibitor-bound states. (B and C) Electron-density maps observed for the sodium binding site. Sodium ions and water molecules are given as big and small spheres, respectively. The 2Fo–Fc simulated annealing composite-omit electron-density maps are given as blue-colored mesh and are contoured at 1.0 σ. (B) Unliganded furin. (C) Furin complexed with MI-52.
Reaction of Furin with Nonspecific Inhibitors.
Previous studies had demonstrated a lack of reactivity of furin for nonspecific covalent serine protease inhibitors (22). We have reanalyzed here the inihibitory potency of DFP, 4-(2-aminoethyl)benzensulfonylfluorid (AEBSF), and PMSF. All three inhibitors readily inhibited the activity of the two prototypical serine proteases, trypsin and subtilisin, to below 3% of their original activity, but did not significantly affect the activity of human furin (SI Materials and Methods). As modeling excluded steric reasons, the failure of these inhibitors to bind may reflect the electronic properties and activation state of furin’s active site, and thus represent an electrophilic probe and measure for the reactivity of the protease.
Calcium-Dependent Activity Regulation of Furin.
Previous studies have shown that the activity of furin is dependent on the presence of calcium (22