Supporting Information Quantitative characterization of the binding and unbinding of millimolar drug fragments with molecular dynamics simulations

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1 Supporting Information Quantitative characterization of the binding and unbinding of millimolar drug fragments with molecular dynamics simulations Simulation Details All binding simulations were run on Anton, a specialized machine for molecular dynamics simulations, 1 using the Amber ff99sb*-ildn 2 4 force field for the protein and the generalized Amber force field (GAFF 5 ), with atomic charges determined by restrained electrostatic potential fit (RESP 6 ), for the ligands. The Amber ff99sb*-ildn force field has been shown to perform well for soluble, folded proteins. 7 Ligand parameters are available upon request. The DMSO and DSS simulations were initiated from the corresponding bound crystal structures (PDB IDs: 1D7H and 1D7I 8 ). The BUT, THI, PROP, and DAP simulations were initiated from the 1D7H structure after deleting the DMSO ligand and placing a single ligand approximately 20 Å from the binding pocket (see Fig. 1 for ligand structures and abbreviations). Because reversible binding was observed in all simulations, the initial starting structure is unlikely to influence the results. Lys, Arg, Asp, and Glu residues as well as the N and C termini were simulated in their charged states, and all His residues were neutral. Torsional backbone corrections U = k ( 1) m 1 [(1 + cos m(φ φ )) / m!] (M = 6, k = 4 kcal mol 1 ), centered at φ = φ xtal 180, were applied to the φ and ψ backbone dihedrals of residues GLY83, GLY86 and GLY89 to prevent degradation of the 80s loop of FKBP on the microsecond timescale. 9 Protein-ligand systems were then solvated in a box of 150 mm NaCl solution initially measuring approximately 64 Å 3 and containing ~24,300 atoms.

2 Each system was equilibrated in the NPT ensemble for 50 ns with harmonic position restraints on all heavy protein and ligand atoms, tapered linearly to 0 from 5 kcal mol 1 Å 2. Production runs were subsequently performed in the NVT ensemble from the final frame of the NPT relaxation simulation by coupling the system to a Nosé-Hoover thermostat 10,11 at 300 K with a relaxation time of 1 ps. A RESPA integrator 12 was used with a time step of 2 fs, and long-range electrostatics were computed every 6 fs. Bonds involving hydrogen atoms were restrained to their equilibrium lengths using the M SHAKE algorithm. 13 Trajectory frames were recorded every 180 ps of simulation. Nonbonded interactions were cut off at 13.5 Å, and long-range electrostatics were computed using the k-space Gaussian split Ewald method 14 with a grid, σ = 2.95 Å, and σ s = 1.89 Å. Starting configurations, with force field information, are available as part of the SI. Trajectories are available upon request. Analysis of MD Simulations Distance and root-mean-square deviation (RMSD) measurements were computed using the HiMach parallel analysis framework. 15 Ligand RMSDs were calculated for the heavy atoms of the ligand after aligning the protein C α atoms near the binding site (FKBP residues 26, 28, 36, 37, 46, 54, 55, 56, 59, 82, 87, and 99) to the corresponding crystal structure. VMD 16 was used to visualize trajectories and to produce molecular images. To calculate the dissociation constant, K D, and binding free energy, ΔG b, from the reversible binding simulations, we use the expressions 17 ln, 2

3 where P u is the fraction of simulation time in which the protein and ligand are unbound, P b is the fraction of simulation time in which the protein and ligand are bound, v is the volume of the simulation box, c o is a standard-state concentration (1 mol L 1 ), N Av is Avogadro s number, k B is Boltzmann s constant, and T is the temperature. In computing equilibrium binding constants for comparison with free energy perturbation (FEP) calculations, there is a subtle difference in the treatment of molecular concentration between our simulations and the experiments. In experimental binding assays, the concentration of the ligand molecule is typically in large excess over that of the protein, such that the concentration of the ligand molecule free in the solution and available for binding to the protein is approximately the same as the total concentration of the ligand. In contrast, our simulations contain only one ligand and one protein, so no free ligand is available to bind to the protein when a ligand molecule is already associated with the protein surface. Since FEP calculates the free energy of ligand binding from the bulk to the binding site without consideration of any protein-associated states, protein-associated states were excluded from the definitions of the bound and unbound states in the reversible binding simulations. To partition trajectories into bound, unbound, and associated states, we calculated the closest distance between the heavy atoms of the ligand and the side chain of TRP59 in the FKBP binding pocket, and the closest distance between the heavy atoms of the ligand and all protein heavy atoms. These time series were smoothed with a 1.8-ns window moving average and used to partition simulation frames into bound states (frames with a ligand-trp59 distance <6 Å), protein-associated states (frames that were not bound, but had a ligand-protein distance <4 Å), and unbound states (all other frames). Errors were calculated over blocks of ~2 µs in length. We also calculated the binding free energy while including the protein-associated states. That is, we defined bound states to be frames with a ligand-trp59 distance <6 Å, and unbound states to be all other frames. Bound states were only located within basin S0a in Fig. 3A. The 3

4 dissociation constants,, and binding free energies,, estimated in this way differed very little from those calculated without the associated state (see Table S1). In this calculation, was calculated as a ratio of the on-rate and off-rate:, where k off was calculated as the inverse of the average bound times, t off, and k on was calculated as the inverse of the average unbound times, t on :. Error estimates were calculated as standard errors of the mean. Specifically, standard errors of the mean were calculated for t on and t off, and then propagated to, k on, and k off. Kinetic values were only calculated with the associated state included. Simulation values for all ligands are reported in Table S1. Free Energy Perturbation Calculations Free energy perturbation calculations were performed using the double-annihilation method, 18 in which the free energy of ligand binding is computed as the free energy difference between the transfer of the ligand from vacuum into the protein binding site, and the transfer from vacuum into aqueous solution. To compute each transfer free energy, a number of intermediate systems were simulated. The simulations were parameterized by (λ q, λ vdw ), in which the charges on the ligand atoms were scaled by λ q, and the Lennard-Jones interactions between the ligand and the rest of the system were modeled using a softcore potential: 19 4

5 4 / /, with α = 0.5. The free-energy difference between the system with λ vdw = 0, λ q = 0 and the system with λ vdw = 1, λ q = 1 was computed for both the ligand in the protein binding site, ΔG protein, and the ligand in the aqueous solution, ΔG aqueous ; the difference between these two values, ΔG protein ΔG aqueous, corresponds to the free energy of binding. In simulations of the ligand in the protein binding site and λ < 1, λ q < 1, restraints were added to prevent the ligand from leaving the binding pocket; the contribution of these restraints to the free energy was corrected using a closed form. 18 Intermediates were selected to minimize the statistical uncertainties in the estimated free energies, following a previously outlined procedure. 20 All of the intermediates were simulated in parallel in a replica exchange simulation, with exchanges between adjacent intermediates attempted every 1 ps. Simulations were run with Desmond 21 in the NPT ensemble at temperature 300 K and pressure of 1 bar. Simulations of the ligand in aqueous solution were run for 10 ns per replica; simulations of the ligand in the protein binding site were run for ns. The short residence times of the weakest binders necessitated running multiple short simulations; the data from these replicates were pooled for analysis. The free-energy differences between adjacent intermediates were computed using the Bennett acceptance ratio method; 22 statistical uncertainties were estimated by dividing the data into five equal time intervals and computing the standard deviation in the free energies between the intervals. Corrections for cutoff dispersion interactions In the reversible binding simulations, Lennard-Jones interactions were not computed between atom pairs separated beyond the nonbonded cutoff r c = 13.5 Å. In free energy calculations, the cutoff is at a shorter r c = 9 Å. Truncating the interactions creates a discontinuity in the potential energy at the point where a pair of atoms is separated by r c (Fig. S4). Because of this 5

6 discontinuity, the force due to Lennard-Jones interactions is not integrated across r c in simulation; the simulations effectively sample a shifted potential, 0,. All free energy perturbation simulations were performed with this shifted potential. To include the contribution of the interactions beyond r c = 9 Å, the energies for the trajectory frames of the two end systems (i.e., with λ vdw = 0, λ q = 0, and with λ vdw = 1, λ q = 1) are recomputed using a larger cutoff r c = 13 Å (beyond which the Lennard-Jones interactions are negligible), and the difference between the energies computed at r c = 9 Å and r c = 13 Å,, is used to estimate the long-range dispersion correction 23 to the binding free energies using the perturbation formula exp exp. Corrections for charged ligands Simulations of periodic systems must be charge-neutral; this presents a difficulty when computing the binding free energy of a ligand with net charge q 0, since in intermediates with λ q < 1, the system has net charge (λ q 1)q. 24 To compensate, the Ewald summation introduces a compensating background charge (sometimes referred to as a gellium ) that is uniformly distributed throughout the simulation box and totals (1 λ q )q. Although this background charge is uniform, and thus does not contribute to the forces, it creates spurious interactions with no counterpart in reversible binding simulations. Specifically, the background charge permeates space, such as the interior volume of atoms, where a discrete counter-ion could not penetrate. The spurious interactions cause incorrect free energy estimates for charged ligands: In the case of the protonated DAP (with +1 net charge), for example, the binding free energy estimated by FEP using the uniform background charge is kcal mol 1, which is different from the value estimated from the reversible binding simulation ( kcal mol 1 ). To avoid 6

7 introducing a uniform background charge, when the charges of the protonated DAP (+1) were scaled by λ q, we also scaled the charges of a randomly selected bulk chloride ion ( 1) by λ q. Although this correction scheme does not correct for the long-range polarization artifacts imposed by periodicity, as is done in an alternative approach, 24 such artifacts have the same contribution to both the FEP and the reversible binding simulations, and thus do not affect the comparison between the two; given the high dielectric of water, the contributions of such artifacts are likely to be negligible in our calculations. 25 The binding free energy for the protonated DAP estimated by FEP with this correction is kcal mol 1, in good agreement with that estimated from the reversible binding simulation. 7

8 References 1. Shaw, D. E.; Dror, R. O.; Salmon, J. K.; Grossman, J. P.; Mackenzie, K. M.; Bank, J. A.; Young, C.; Deneroff, M. M.; Batson, B.; Bowers, K. J.; Chow, E.; Eastwood, M. P.; Ierardi, D. J.; Klepeis, J. L.; Kuskin, J. S.; Larson, R. H.; Lindorff-Larsen, K.; Maragakis, P.; Moraes, M. A.; Piana, S.; Shan, Y.; Towles, B. Millisecond-scale molecular dynamics simulations on Anton. Proceedings of the Conference on High Performance Computing, Networking, Storage and Analysis (SC09) 2009, New York, NY: ACM. 2. Hornak, V.; Abel, R.; Okur, A.; Strockbine, B.; Roitberg, A.; Simmerling, C. Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins 2006, 65, Best, R. B.; Hummer, G. Optimized molecular dynamics force fields applied to the helix coil transition of polypeptides. J. Phys. Chem. B. 2009, 113, Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99sb protein force field. Proteins 2010, 78, Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general Amber force field. J. Comp. Chem. 2004, 25, Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model. J. Phys. Chem. 1993, 97, Piana, S.; Klepeis, J. L.; Shaw, D. E. Assessing the accuracy of physical models used in protein-folding simulations: quantitative evidence from long molecular dynamics simulations. Curr. Opin. Struct. Biol. 2014, 24, Burkhard, P.; Taylor, P.; Walkinshaw, M. D. X-ray structures of small ligand-fkbp complexes provide an estimate for hydrophobic interaction energies. J. Mol. Biol. 2000, 295(4),

9 9. Jensen, M. Ø.; Jogini, V.; Borhani, D. W.; Leffler, A. E.; Dror, R. O.; Shaw, D. E. Mechanism of voltage gating in potassium channels. J. Phys. Chem., 1993, 97(40), Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 1985, 31(3), Tuckerman, M.; Berne, B. J.; Martyna, G. J. Reversible multiple time scale molecular dynamics. J. Chem. Phys. 1992, 97(3), Lippert, R. A.; Bowers, K. J.; Dror, R. O.; Eastwood, M. P.; Gregersen, B. A.; Klepeis, J. L.; Kolossvary, I. A common, avoidable source of error in molecular dynamics integrators. J. Chem. Phys. 2007, 126(4), Shan, Y.; Klepeis, J. L.; Eastwood, M. P.; Dror, R. O.; Shaw, D. E. Gaussian split Ewald: A fast Ewald mesh method for molecular simulation. J. Chem. Phys. 2005, 122(5), Tu, T.; Rendleman, C. A.; Borhani, D. W.; Dror, R. O.; Gullingsrud, J.; Jensen, M. Ø.; Klepeis, J. L.; Maragakis, P.; Miller, P.; Stafford, K. A.; Shaw, D. E. A scalable parallel framework for analyzing terascale molecular dynamics simulation trajectories. Proceedings of the ACM/IEEE Conference on Supercomputing (SC08) 2008, New York, NY: ACM. 16. Humphrey, W.; Dalke, A.; Schulten, K. VMD Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, De Jong, D. H.; Schäfer, L. V.; De Vries, A. H.; Marrink, S. J.; Berendsen, H. J.; Grubmüller, H. Determining equilibrium constants for dimerization reactions from molecular dynamics simulations. J. Comput. Chem. 2011, 32(9),

10 18. Boresch, S.; Tettinger, F.; Leitgeb, M.; Karplus, M. Absolute binding free energies: a quantitative approach for their calculation. J. Phys. Chem. B 2003, 107(35), Beutler, T. C.; Mark, A. E.; van Schaik, R. C.; Gerber, P. R.; van Gunsteren, W. F. Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations. Chem. Phys. Lett. 1994, 222(6), Shenfeld, D. K.; Xu, H.; Eastwood, M. P.; Dror, R. O.; Shaw, D. E. Minimizing thermodynamic length to select intermediate states for free-energy calculations and replica-exchange simulations. Phys. Rev. E 2009, 80, Bowers, K. J.; Chow, E.; Xu, H.; Dror, R. O.; Eastwood, M. P.; Gregersen, B. A.; Klepeis, J. L.; Kolossvary, I.; Moraes, M. A.; Sacerdoti, F. D.; Salmon, J. K.; Shan, Y.; Shaw, D. E. Scalable algorithms for molecular dynamics simulations on commodity clusters. Proceedings of the ACM/IEEE Conference on Supercomputing (SC06) 2006, New York, NY: IEEE. 22. Bennett, C. H. Efficient estimation of free energy differences from Monte Carlo data. Phys. Procedia 1976, 22(2), Shirts, M. R.; Mobley, D. L.; Chodera, J. D.; Pande, V. S. Accurate and efficient corrections for missing dispersion interactions in molecular simulations. J. Phys. Chem. B 2007, 111, Rocklin, G. J.; Mobley, D. L.; Dill, K. A.; Hunenberger, P. H. Calculating the binding free energies of charged species based on explicit-solvent simulations employing latticesum methods: An accurate correction scheme for electrostatic finite-size effects. J. Chem. Phys. 2013, 139, Lin, Y.-L.; Aleksandrov, A.; Simonson, T.; Roux, B. An overview of electrostatic free energy computations for solutions and proteins. J. Chem. Theory Comput. 2014, 10, Jones, E.; Oliphant, E.; Peterson, P.; et al. SciPy: Open source scientific tools for Python , 10

11 27. Bierer, B. E.; Mattila, P. S.; Standaert, R. F.; Herzenberg, L. A.; Burakoff, S. J.; Crabtree, G.; Schreiber, S. L. Two distinct signal transmission pathways in T lymphocytes are inhibited by complexes formed between an immunophilin and either FK506 or rapamycin. Proc. Natl. Acad. Sci. U. S. A. 1990, 87, Schreiber, S. L. Chemistry and biology of the immunophilins and their immunosuppressive ligands. Science 1991, 251,

12 Supporting Table and Figures Ligand abbrev. N atoms N b Time (µs) ΔG b (kcal mol 1 ) K D (mm) ΔH b (kcal mol 1 ) (kcal mol 1 ) (mm) k on (M 1 s 1 ) k off (s ) DMSO (1) 110(20) 2(1) 1.52(7) 79(9) 0.75(7) 59(5) PROP (1) 100(30) 5(1) 1.6(1) 70(12) 0.81(9) 56(8) DSS (1) 9(2) 4.1(8) 2.75(8) 10(1) 2.1(2) 21(2) BUT (6) 38(4) 2.8(8) 1.97(6) 37(4) 1.23(8) 45(4) THI (1) 5(1) 4.4(7) 3.2(1) 4.5(8) 1.7(2) 7.4(8) DAP (1) 1.8(4) 2(1) 3.5(1) 2.7(7) 3.2(7) 9(1) DAPP (9) 110(20) 0(2) 1.38(9) 100(15) 1.2(1) 120(10) 12

13 Table S1. Expanded summary of the thermodynamic and kinetic parameters calculated from fragment binding MD simulations. N atoms is the number of heavy atoms in the ligand; N b is the total number of reversible binding events observed in the simulations; Time is the total simulation time; ΔG b is the free energy of binding; K D is the dissociation constant; ΔH b is the enthalpy of binding calculated from the difference in the average potential energy between the bound and unbound states; and are the free energy of binding and the dissociation constant, respectively, including the associated state (see SI text); k on and k off are the on- and off-rates. Structures and full names of the ligands are given in Fig

14 Figure S1. Ligand fragments reversibly bind to the receptor and exist in at least two heavily populated poses once bound. (A) RMSD of the heavy atoms of the ligand fragment DSS from the FKBP-DSS crystal structure (PDB ID 1D7I), calculated after aligning on protein binding pocket Cα atoms (residue IDs 26, 28, 36, 37, 46, 54, 55, 56, 59, 82, 87, and 99). Only the first 2 µs of the 20 µs simulation are shown for clarity. This behavior is typical of the other ligand fragments. (B) Probability density of the ligand RMSD for DSS, DMSO, and BUT at low RMSD values. The RMSDs for DMSO and BUT were calculated as in (A) for DSS, except that the FKBP-DMSO (PDB ID 1D7H) and FKBP-BUT (PDB ID 1D7J) crystal structures, respectively, were used as references. The presence of multiple peaks indicates multiple stable poses. 14

15 Figure S2. In addition to binding in the crystallographically determined binding site, drug fragments often explore several alternative binding sites. These six contour maps show 15

16 projections of the x and y components of the center-of-mass position density of DMS, PRP, THI, DSS, DAP, and DAPP as free energy surfaces. These surfaces display features similar to those in Fig. 3A for BUT. Surfaces were constructed by binning the center-of-mass positions of ligands into a 2D histogram along x and y and then smoothing with a kernel density estimator using a Gaussian kernel. 26 The resulting histograms were then Boltzmann inverted and linearly shifted such that their minima were at zero. 16

Figure S3. Fragments are able to map out regions of the protein capable of potent binding. Structures of FK506 (left, PDB ID 1FKF, K D = 0.4 nm) and rapamycin (right, PDB ID 1FKB, K D = 0.

17 Figure S3. Fragments are able to map out regions of the protein capable of potent binding. Structures of FK506 (left, PDB ID 1FKF, K D = 0.4 nm) and rapamycin (right, PDB ID 1FKB, K D = 0.2 nm 27,28 ) bound to FKBP overlaid onto regions of high BUT fragment occupancy S0a, S0b, and S0c (cf., Fig. 3). To construct the fragment density, the center-of-mass position of BUT was binned and then smoothed with a kernel density estimator using a Gaussian kernel. 26 The resulting histogram was then Boltzmann inverted and linearly shifted such that its minimum was at zero. Black, red, blue, and green contours are spaced at 1 kcal mol 1 intervals. 17

18 Figure S4. The shifted Lennard-Jones potential used in the MD simulations due to cut-off longrange interactions. (A) The Lennard-Jones potential (green), the potential computed during simulation, cut off at r c (blue), and the effective shifted potential V shift (red) that is sampled due to computation of interactions only within r c. (B) The force due to the Lennard-Jones potential (green) and the effective force (red) in simulation when interactions are cut off at r c. 18

Supporting Material for. Microscopic origin of gating current fluctuations in a potassium channel voltage sensor

Supporting Material for. Microscopic origin of gating current fluctuations in a potassium channel voltage sensor Supporting Material for Microscopic origin of gating current fluctuations in a potassium channel voltage sensor J. Alfredo Freites, * Eric V. Schow, * Stephen H. White, and Douglas J. Tobias * * Department