Cooperative Binding of the Cationic Porphyrin Tris-T4 Enhances Catalytic Activity of 20S Proteasome Unveiling a Complex Distribution of Functional States

The present study provides new evidence that cationic porphyrins may be considered as tunable platforms to interfere with the structural “key code” present on the 20S proteasome α-rings and, by consequence, with its catalytic activity. Here, we describe the functional and conformational effects on the 20S proteasome induced by the cooperative binding of the tri-cationic 5-(phenyl)-10,15,20-(tri N-methyl-4-pyridyl) porphyrin (Tris-T4). Our integrated kinetic, NMR, and in silico analysis allowed us to disclose a complex effect on the 20S catalytic activity depending on substrate/porphyrin concentration. The analysis of the kinetic data shows that Tris-T4 shifts the relative populations of the multiple interconverting 20S proteasome conformations leading to an increase in substrate hydrolysis by an allosteric pathway. Based on our Tris-T4/h20S interaction model, Tris-T4 is able to affect gating dynamics and substrate hydrolysis by binding to an array of negatively charged and hydrophobic residues present on the protein surface involved in the 20S molecular activation by the regulatory proteins (RPs). Accordingly, despite the fact that Tris-T4 also binds to the α3ΔN mutant, allosteric modulation is not observed since the molecular mechanism connecting gate dynamics with substrate hydrolysis is impaired. We envisage that the dynamic view of the 20S conformational equilibria, activated through cooperative Tris-T4 binding, may work as a simplified model for a better understanding of the intricate network of 20S conformational/functional states that may be mobilized by exogenous ligands, paving the way for the development of a new generation of proteasome allosteric modulators.


S4
The resulting PM7 conformers were subsequently ranked as reported above for MM conformers. The global minimum conformer of Tris-T4 was selected for the dynamic docking studies in complex with human 20S.
Docking studies on human 20S proteasome. Docking calculations were performed by using our previously developed atomic models of human 20S in the closed and open conformational states 5 . It has to be underlined that, since we used as template for human 20S in the open state the structure determined by Chen et al. by cryo-electron microscopy (cryoEM) 6 , then, our atomic model of human 20S in the open state is composed by just one "half" (one -ring and one -ring) of the entire 20S structure.
The four starting structures to be used in docking studies were generated by positioning: i) one Tris-T4 molecule at α5-α6 groove (closed state); ii) one Tris-T4 at α4-α5 (open state); iii) three Tris-T4 molecules bound at α1-α2, α4-α5 and α5-α6 grooves (closed and open states). The starting complexes were then subjected to dynamic docking studies (Affinity, SA_Docking; Insight2005, Accelrys, San Diego). In particular, a docking methodology, which considers all the systems flexible (i.e., ligand and protein), was used. During the first step, in the starting structures, the ligand was moved by a random combination of translation, rotation, and torsional changes to sample both the conformational space of the ligand and its orientation with respect to the binding domain area (MxRChange = 3 Å; MxAngChange = 180°). The binding domain area was defined as a subset including all residues of human 20S proteasome. Thus, all proteasome atoms were left free to move during the entire course of docking calculations, whereas, in order to avoid unrealistic results during the subsequent SA calculations, a tethering restraint was applied on the SCRs of the protein (defined below).

S5
During the Monte Carlo/Metropolis docking step, van der Waals (vdW) and Coulombic terms were scaled to a factor of 0.1 to avoid very severe divergences in the vdW and Coulombic energies. If the energy of a complex structure resulting from random moves of the ligand was higher by the energy tolerance parameter than the energy of the last accepted structure, it was not accepted for minimization. To ensure a wide variance of the input structures to be successively minimized, an energy tolerance value of 10 6 kcal/mol from the previous structure was used. After the energy minimization step (conjugate gradient; 2500 iterations; ε = 1), the energy test, with an energy range of 50 kcal/mol, and a structure similarity check (rms tolerance = 0.3 kcal/Å) was applied to select the 20 acceptable structures. Each subsequent structure was generated from the last accepted structure.
Following this procedure, the resulting docked structures were ranked by their conformational energy and were analyzed considering the non-bonded interaction energies between the ligand and the enzyme (vdW and electrostatic energy contribution; Group Based method 9 ; CUT_OFF = 100; ε = 2*r; Discover_3 Module of Insight2005).
The Monte Carlo docked complexes were then subjected to molecular dynamics simulations at flexible temperatures (Simulated Annealing, SA) to enhance the fixing of the ligand into the binding site and to explore possible ligand-induced large-scale conformational changes of the protein. In particular, the resulting docked complexes were subjected also to a molecular dynamics SA protocol using the Cell_Multipole method for non-bonded interactions and the dielectric constant of the water (ε = 80*r). A tethering restraint was applied on the SCRs of the complex. The set of structural restraints applied was the same as for previous docking calculations. The protocol included 5 ps of a dynamic run divided in 50 stages (100 fs each) during which the temperature of the system was linearly decreased from 500 to 300 K (Verlet velocity integrator; time step = 1.0 fs). In simulated annealing, the temperature is altered in time increments from an initial temperature to a final temperature. The temperature is changed by adjusting the kinetic energy of the structure (by rescaling the velocities of the atoms). Molecular dynamics calculations were performed using a constant temperature and constant volume (NVT) statistical ensemble, and the direct velocity scaling as temperature control method (temp S6 window = 10 K). In the first stage, initial velocities were randomly generated from the Boltzmann distribution, according to the desired temperature, while during the subsequent stages initial velocities were generated from dynamics restart data. The temperature of 500 K was applied with the aim of surmounting torsional barriers, thus allowing an unconstrained rearrangement of the "ligand" and the "protein" binding site (initial vdW and Coulombic scale factors = 0.1). Successively temperature was linearly reduced to 300 K in 5 ps, and, concurrently, the vdW and Coulombic scale factors have been similarly increased from their initial values (0.1) to their final values (1.0). A final round of 10 5 minimization steps (ε = 80*r) followed the last dynamics steps, and the minimized structures were saved in a trajectory file. The ligand/enzyme complexes thus obtained were ranked by their conformational energy and analyzed considering the non-bonded interaction energies between the ligand and the enzyme (vdW and electrostatic energy contribution; Group Based method; CUT_OFF = 100; ε = 2*r; Discover_3 Module of Insight2005). The complex with the best compromise between the non-bonded interaction energies obtained by Monte Carlo and SA calculations was selected as the structure representing the most probable binding mode. In order to allow the whole relaxation of the protein, the selected annealed complexes were then subjected to MM energy minimization without restraints (Steepest Descent algorithm; ε = 80*r) until the maximum RMS derivative was less than 0.5 kcal/Å (Module Discover; Insight 2005). The protein structural quality in the resulting complexes was then checked using Molprobity structure evaluator software 10 and compared to that of the reference PDB structure.
The SCRs of the human 20S proteasome were identified using the Structure Prediction and Sequence Analysis server PredictProtein (http://www.predictprotein. org/) and are reported in Table S15. Within the identified SCRs, the following restraints were used: the distance between backbone hydrogen bond donors and acceptors in the alphahelices was restrained within 2.5 Å. On the other hand, the φ and ψ torsional angles of the beta-sheets were restrained to -119° and +113°, or -139° and +135°, respectively, according to the presence of a parallel or anti-parallel structure. In particular, according to the reliability index values obtained from the secondary structure prediction, the following set S7 of force constant values were applied (quadratic form) : i) 1 kcal/mol/Å 2 (maximum force: 10 kcal/mol/Å 2 ) for reliability index values from 0 to 3, ii) 10 kcal/mol/Å 2 (maximum force: 100 kcal/mol/Å 2 ) for reliability index values from 4 to 6, and iii) 100 kcal/mol/Å 2 (maximum force: 1000 kcal/mol/Å 2 ) for reliability index values from 7 to 9. CAVER 12 was used to identify tunnels considered as void pathways leading from a cavity buried in protein core to the bulk solvent. Tunnels were generated selecting as starting point the center of gravity of all residues within 5 Å from the β5-Thr1 (i.e, R19, A20, V31, K33, S8 A46, G47, G48, A49, C52) (max distance = 3.0 Å and desired radius = 5.0 Å). Tunnels were generated using the following parameters: 0.9 Å for probe radius (minimum radius of the tunnel), 2.0 Å for shell depth (maximal depth of a surface region) and 3.0 Å for shell radius (radius of the shell probe used to define the bulk solvent). Tunnel clustering was performed by the average-link hierarchical algorithm selecting 2.0 Å for the calculation of pairwise tunnel distances (i.e. dissimilarities) as the cutoff able to capture all the representative directions of the identifies tunnels.

Structural investigation
.083 a Both the wild-type and the α3ΔN mutant; the amino acids not conserved between human and yeast 20S proteasome (alignment performed using PROMALS3D server) are evidenced in bold. b 19S functional states involved in the reported interaction are specified in brackets. c Amino acids of the C-terminal tail of Rpt5 (aa426-aa439; α5/α6) (19S) and PA200 (aa1830-aa1843) having at least one atom within a 4 Å radius from any given h20S residue. d Negatively charged residues involved in ionic interaction with RPs (i.e., PA28, PA200 and 19S).
19S (SA/EA1-2; SB/EB and SC/EC1-2) a Both the wild-type and the α3ΔN mutant; the amino acids not conserved between human and yeast 20S proteasome (alignment performed using PROMALS3D server) are evidenced in bold. b 19S functional states involved in the reported interaction are specified in brackets. c Amino acids of the C-terminal tail of Rpt1 (aa421-aa433; α4/α5) (19S) having at least one atom within a 4 Å radius from any given h20S residue. d Negatively charged residues involved in ionic interaction with RPs (i.e., PA28, PA200 and 19S). Table S11. Ligand-residue non-bond interaction energies (kcal/mol) of the 20S in complex with three molecules of Tris-T4 obtained by Monte Carlo and SA calculations using as starting binding sites the α5-α6, α4-α5 and α1-α2 grooves of 20S in the closed conformation. The residues involved in the interaction with RPs are noted and the RPs are reported. The corresponding wt y20S residues (PROMALS3D alignment; all conserved in the α3ΔN mutant) are also listed.
-0.788 a Both the wild-type and the α3ΔN mutant; the amino acids not conserved between human and yeast 20S proteasome (alignment performed using PROMALS3D server) are evidenced in bold. b 19S functional states involved in the reported interaction are specified in brackets. c Amino acids of the C-terminal tail of Rpt5 (aa426-aa439; α5/α6), Rpt1 (aa421-433; α4/α5), of Rpt3 (aa407-418; α1/α2) (19S) and PA200 (aa1830-aa1843) having at least one atom within a 4 Å radius from any given h20S residue. d Negatively charged residues involved in ionic interaction with RPs (i.e., PA28, PA200 and 19S).        (Table S4) show Tris-T4 bound at the α5-α6 groove (although presenting a different binding mode with respect to the starting position). C) Top view of dynamic docking results without the first ring of α subunits: the last six generated complexes presented the ligand positioned either at the level of the first β-ring or at the interface between the first and the second β-ring (Table S4).The backbone of the starting complex is displayed as solid ribbons and colored in pink (α1), orange (α2), brown (α3), light green (α4), cyan (α5), magenta (α6), and gray (α7, α subunits of the second ring and all β subunits). The backbone of the calculated complexes is displayed as line ribbons and colored in orange (B and C). The porphyrin ligands are colored by atom type (C: green and N: blue) and displayed as CPK. In B the α subunits and the catalytic β subunits are labeled. In C the catalytic β subunits are labeled and colored in pink (β1), violet (β2), and cyan (β5).  Figure S9. A) Dynamic docking results obtained for Tris_T4 using as starting points the α1-α2. α4-α5. and α5-α6 grooves of the closed conformation of human 20S proteasome. B) Top view of dynamic docking results without the two rings of β subunits and the second ring of α subunits. C) Top view of dynamic docking results without the first ring of α subunits. The analysis of the whole of the generated complexes using the 20S closed conformation as starting structure showed that in four of them (2-5 in Table S6) one molecule of Tris-T4 is placed at the level of the first β-ring (A and C). The other two molecules are localized on the α-ring, with one of the two always positioned at α5-α6 groove (B). Finally, in the subsequent four complexes (6-9 in Table S6), all three molecules move down, placing at the interface of the β rings or between the 5 and 6 subunits.
The backbone of the starting complex is displayed as solid ribbons and colored in pink (α1), orange (α2), brown (α3), light green (α4), cyan (α5), magenta (α6), and grey (α7, α subunits of the second ring and all β subunits). The backbone of the calculated complexes is displayed as line ribbons and colored in orange (B and C). The porphyrin ligands are colored by atom type (C: green and N: blue) and displayed as CPK. In B the α subunits and the catalytic β subunits are labeled. In C the catalytic β subunits are labeled and colored in pink (β1), violet (β2), and cyan (β5). Figure S10. A) Dynamic docking results obtained for Tris_T4 using as starting points the α1-α2. α4-α5. and α5-α6 grooves of the open conformation of human 20S proteasome. B) Top view of dynamic docking results without the ring of β subunits. C) Bottom view of dynamic docking results without the ring of β subunits. The ligand molecule bound to the 1-2 groove moves down the interior of the α-ring or toward the center of the protein (A and C). On the other hand, the other two molecules of Tris-T4 in most solutions bind at 4-5 and 5-6 grooves although in some binding poses occupying the substrate channel between the and the -ring or moving along the grooves toward the substrate gate. Interestingly, in four solutions one Tris-T4 binds the negatively charged 5-loop (B). The backbone of the starting complex is displayed as solid ribbons and colored in pink (α1), orange (α2), brown (α3), light green (α4), cyan (α5), magenta (α6), and grey (α7, α subunits of the second ring and all β subunits). The backbone of the calculated complexes is displayed as line ribbons and colored in orange (B and C). The porphyrin ligands are colored by atom type (C: green and N: blue) and displayed as CPK. In B the α subunits and the catalytic β subunits are labeled. : the protein is displayed as Connolly surface and colored in gray; the negatively charged residues involved in ionic interactions with RPs (i.e., 19S, PA28α and PA200) are displayed as CPK and colored in red. C and D: the protein is displayed in ribbons and secondary structure elements of each subunit are sequentially colored from N-to C-terminal end (αH0= blue; αH1= cyan; αH2= magenta, αH3-αH5= light red to dark red).   Table 1. Circles represents different conformational states and the dimension is indicative of their abundance.