A Curvilinear-Path Umbrella Sampling Approach to Characterizing the Interactions Between Rapamycin and Three FKBP12 Variants

Rapamycin is an immunosuppressant macrolide that exhibits anti-proliferative properties through inhibiting the mTOR kinase. In fact, the drug first associates with the FKBP12 enzyme before interacting with the FRB domain of its target. Despite the availability of structural and thermodynamic information on the interaction of FKBP12 with rapamycin, the energetic and mechanistic understanding of this process is still incomplete. We recently reported a multiple-walker umbrella sampling simulation approach to characterizing the protein–protein interaction energetics along curvilinear paths. In the present paper, we extend our investigations to a protein-small molecule duo, the FKBP12•rapamycin complex. We estimate the binding free energies of rapamycin with wild-type FKBP12 and two mutants in which a hydrogen bond has been removed, D37V and Y82F. Furthermore, the underlying mechanistic details are analyzed. The calculated standard free energies of binding agree well with the experimental data, and the roles of the hydrogen bonds are shown to be quite different for each of these two mutated residues. On one hand, removing the carboxylate group of D37 strongly destabilizes the association; on the other hand, the hydroxyl group of Y82 is nearly unnecessary for the stability of the complex because some nonconventional, cryptic, indirect interaction mechanisms seem to be at work.

SUPPLEMENTARY FIGURE S2 | Comparison between the electronic environment of the amide NH bounds in FKBP12WT and FKBP12D37V. (A) 1 H-15 N hetero-nuclear single quantum coherence (HSQC) NMR spectra for the wild-type protein (blue) and for the D37V mutant (pink). Measurements were performed at 298 K on a 600 MHz NMR spectrometer (UltraShield 600 and AVANCE 600 system, Bruker). 15 N-labeled proteins were purified using protocols adapted from the literature 3 and dissolved at 50 µM in a buffer containing 20 mM sodium phosphate pH 7.0 and 100 mM NaCl. (B) Corresponding analysis of the chemical shift perturbations, 4 computed as = √(∆ )² + ( . × ∆ )² with ∆ and ∆ being the respective proton and nitrogen chemical shift difference between the wild-type protein and the mutant one. 5 (C) Structure of FKBP12WT on which the residues highlighted in red are the ones that have a CSP larger than the mean plus two standard deviation upon substitution of D37 by V37, 4  The time at which VDW cancels is converted in CoG distance thanks to the linear relationship between those two parameters (grey diagonal). Then, the cutoff separation distance is computed by simply subtracting to the obtained value the mean CoG distance in the complex at equilibrium: * , = * , − . (B) Same data for FKBP12Y82F•rapamycin. (C) Same data for FKBP12D37V•rapamycin.

SUPPLEMENTRARY FIGURE S8
| Effect of the temperature correction on the experimentally determined binding free energies for the FKBP12 + rapamycin ⇄ FKBP12•rapamycin reaction. Full circles correspond to ∆ , the measurements retrieved from the literature and performed at various temperatures , whereas open circles correspond to ∆ , the same data extrapolated at = 21.85 °C, the temperature at which MD simulations were run (see Supplementary Table S2 for numerical values, for indexing, and for details on the correction procedure). Red markers refer to the wild-type FKBP12, blue ones to the Y82F mutant, and green ones to the D37V mutant. Data have been sorted along the x-axis according to their publication year; moreover, to emphasize on possible biases due to individual practises we have clustered together all measurements coming from a same laboratory. The three colored lines correspond to ∆ 0 , the MD results obtained thanks to the CPUS approach (see Table 1 for numerical values). The four black and dashed lines indicate the ∆ values associated with the 0.1, 1, 10, and 100 nM dissociation equilibrium constants.
SUPPLEMENTARY FIGURE S9 | Comparison of the separation distance patterns obtained during the dissociation of rapamycin from the wild-type FKBP12 and from the Y82F mutant. Pulling on the molecular partners CoG starts at 10 ns. (A) Evolution of the distance between the O3 carbonyl oxygen of rapamycin and the oxygen as well as the six carbons of residue Y82 phenol group in the FKBP12WT•rapamycin complex. Data are provided for all 15 runs and the one associated with the lower-bound PMF profile is in a brighter color. (B) Same plots for the distance between the O3 carbonyl oxygen of rapamycin and the six carbons of residue F82 phenyl group in the FKBP12Y82F•rapamycin complex.
SUPPLEMENTARY FIGURE S10 | Comparison of the separation distance patterns obtained during the dissociation of rapamycin from the wild-type FKBP12 and from the D37V mutant. Pulling on the molecular partners CoG starts at 10 ns. (A) Evolution of the distance between the O6 hydroxyl oxygen of rapamycin and the 2 oxygen of residue D37 carboxyl group in the FKBP12WT•rapamycin complex. Data are provided for all 15 runs and the one associated with the lower-bound PMF profile is in a brighter color. (B) Same plots for the distance between the O6 hydroxyl oxygen of rapamycin and the 2 carbons of residue V37 methyl groups in the FKBP12D37V•rapamycin complex.
SUPPLEMENTARY FIGURE S11 | Curvilinear paths obtained for the FKBP12WT•rapamycin → FKBP12WT + rapamycin dissociation. Each sphere roughly corresponds to the barycenter of all rapamycin CoG extracted from one umbrella sampling window of CPUS MD simulations. It has the same color than the PMF profile it is associated with. The black lines are guides for the eye. Data are only displayed up to = 10 Å.
SUPPLEMENTARY FIGURE S12 | Curvilinear paths obtained for the FKBP12Y82F•rapamycin → FKBP12Y82F + rapamycin dissociation. Each sphere roughly corresponds to the barycenter of all rapamycin CoG extracted from one umbrella sampling window of CPUS MD simulations. It has the same color than the PMF profile it is associated with. The black lines are guides for the eye. Data are only displayed up to = 10 Å.
SUPPLEMENTARY FIGURE S13 | Curvilinear paths obtained for the FKBP12D37V•rapamycin → FKBP12D37V + rapamycin dissociation. Each sphere roughly corresponds to the barycenter of all rapamycin CoG extracted from one umbrella sampling window of CPUS MD simulations. It has the same color than the PMF profile it is associated with. The black lines are guides for the eye. Data are only displayed up to = 10 Å.
SUPPLEMENTARY FIGURE S14 | Comparison between the curvilinear paths of dissociation corresponding to lower-bound PMF profiles (top) and to highest PMF profiles (bottom). Images for FKBP12WT•rapamycin (left), FKBP12Y82F•rapamycin (middle), and FKBP12D37V•rapamycin (right) were extracted from Supplementary Figures S11, S12, and S13, respectively. Red circles highlight stagnation areas along the dissociation paths.
SUPPLEMENTARY FIGURE S15 | Evolution of rapamycin conformation during its dissociation from FKBP12WT. The root-mean-square deviation was computed on all the heavy atoms of the macrolide (i.e. C, N, and O) and the conformation in the FKBP12WT•rapamycin crystal pose (PDB 1FKB) was taken as reference. Pulling on the molecular partners CoG starts at 0 ns. SUPPLEMENTARY FIGURE S16 | Evolution of rapamycin conformation during its dissociation from FKBP12Y82F. The root-mean-square deviation was computed on all the heavy atoms of the macrolide (i.e. C, N, and O) and the conformation in the FKBP12WT•rapamycin crystal pose (PDB 1FKB) was taken as reference. Pulling on the molecular partners CoG starts at 0 ns. SUPPLEMENTARY FIGURE S17 | Evolution of rapamycin conformation during its dissociation from FKBP12D37V. The root-mean-square deviation was computed on all the heavy atoms of the macrolide (i.e. C, N, and O) and the conformation in the FKBP12WT•rapamycin crystal pose (PDB 1FKB) was taken as reference. Pulling on the molecular partners CoG starts at 0 ns. SUPPLEMENTARY TABLE S1 | Cutoff separation distance and binding free energies obtained from the 15 independent runs of CPUS MD simulations performed on the complexes formed between rapamycin and each of the three FKBP12 variants. The lower-bound PMFs have been highlighted in bold and with the same color as in the plots (see Figure 2).  Figure S8, the usual ± 0.1 to ± 0.5 °C specification given for most apparatuses would result in minute changes for the binding free energy. When the error on was specified it was propagated according to ∆ = ⁄ and ∆ ² = ( ⁄ )² + ∆ ² × (1 − ⁄ )². 29 Conversely, we did not report any error on ∆ when the uncertainty on was not indicated; indeed, the influence of ∆ is very limited and the resulting small ∆ values would not account for the reality of the measurements. When a range was provided for we first converted it by taking the mean of the extremal values as a central value and the full range as error bar, then we performed the computation of both ∆ and ∆ . c Rapamycin = sirolimus is registered under ID BDBM36609 in BindingDB (www.bindingdb.org) and all values reported in this databank have been included in the present Table. d Unless otherwise specified, the titrant is rapamycin. In inhibition assays it competes with peptidic substrates of FKBP12 and thus prevents their isomerization; in competitive titrations it binds to the same pocket as the tracers and thus favors the disruption of the indicated complexes. Various mathematical models can be used to analyze the results of these assays and sometimes the authors do not provide the equilibrium dissociation constant but parameters such as the inhibitor constant, , or the half maximal inhibitory concentration activity, 50 . Although the two latter parameters are not identical to it is here assumed that if appropriate conditions have been selected to run the experiment they offer a fair estimate of it (at least within the same order of magnitude). e Only the buffering system and the major salts are provided. Among the other components one may find DTT and EDTA (at millimolar concentrations), glycerol used for stabilization purpose (at up to more than 10 %), and organic solvents (e.g. methanol, ethanol, or DMSO) used to dissolve rapamycin (at up to a few %). f This parameter is sometimes not specified (NS) or just indicated as "room temperature" (RT); in both cases, we assumed measurements were performed around 20 -25 °C, i.e. = = 21.85 °C. As evidenced on Supplementary Figure S8 a 2 to 3 °C imprecision on temperature should not result in too large changes for the binding free energy. g Values between parentheses are hypothesized to be of low quality by the researchers that collected them, the reason of which been given in the adjacent column. Values between double parentheses were inferred by ourselves from the graphical data displayed in the cited article. Values between brackets partly rely on data sets published in other articles, the corresponding reference been given in the adjacent column. h This index is used to plot Figure 2D and Supplementary Figure S8.