How To, Education & Training

Absolute Binding Free Energy Calculations of Sparsomycin Analogs to the Bacterial Ribosome

Description
Absolute Binding Free Energy Calculations of Sparsomycin Analogs to the Bacterial Ribosome
Published
of 15
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  Absolute Binding Free Energy Calculations of Sparsomycin Analogs to the BacterialRibosome Xiaoxia Ge † and Benoı ˆt Roux* ,‡,§  Department of Physiology and Biophysics, Weill Medical College of Cornell Uni V ersity, New York, New York 10065, Department of Biochemistry and Molecular Biology, The Uni V ersity of Chicago, 929 East 57th Street,Chicago, Illinois 60637, and Biosciences Di V ision, Argonne National Laboratory, 9700 South Cass A V enue, Argonne, Illinois 60439 Recei V ed: January 20, 2010; Re V ised Manuscript Recei V ed: June 1, 2010 The interactions of the 50S subunit of bacterial ribosome with antibiotic sparsomycin (SPS) and five analogs(AN) are investigated through the calculation of the standard (absolute) binding free energy and thecharacterization of conformational dynamics. The standard binding free energies of the complexes are computedusing free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. Restrainingpotentials are applied and then released during the simulation to efficiently sample the changes in translational,orientational, and conformational freedom of the ligand and receptor upon binding. The biasing effects of therestraining potentials are rigorously removed. The loss of conformational freedom of the ligand upon bindingis determined by introducing a potential of mean force (PMF) as a function of the root-mean-square deviation(rmsd) of the ligand relative to its conformation in the bound state. To reduce the size of the simulatedsystem, the binding pocket of the ribosome is simulated in the framework of the generalized solvent boundarypotential (GSBP). The number of solvent molecules in the buried binding site is treated via grand canonicalMonte Carlo (GCMC) during the FEP/MD simulations. The correlation coefficient between the calculatedand measured binding free energies is 0.96, and the experimentally observed ranking order for the bindingaffinities of the six ligands is reproduced. However, while the calculated affinities of the strong binders agreewell with the experimental values, those for the weak binders are underestimated. Introduction The ribosome is the largest and most complex enzyme innature. Ribosomes synthesize proteins in every cell of all livingorganisms. These complicated molecular machines comprise twononequivalent subunits composed of RNA strands and more than50 different proteins with a total mass of over 2.5 MDa. The30S small subunit functions mainly to decode the geneticinformation in mRNA and control the translation fidelity. 1,2 The50S large subunit performs the main ribosomal catalytic functionin the peptidyl-transferase center (PTC) and provides the proteinexit tunnel. The tRNA substrates join the two subunits at eachof their three binding sites, A (aminoacyl), P (peptidyl), and E(exit), and functionally decode the genetic information and carryamino acids to be incorporated in the nascent protein. 3,4 Nearlyhalf of known antibiotic therapeutics target the ribosome.Antibiotics inhibit protein synthesis by interfering with tRNAbinding in either of the ribosomal subunits. 5,6 Among manyribosome-targeting drugs, sparsomycin (SPS) has been used asa cancer drug due to its inhibition activity at peptide bondformation by binding to the PTC of large ribosomal subunit inboth prokaryotic and eukaryotic cells. 7,8 High-resolution crystal structures of ribosome - antibioticcomplexes published in recent years have revolutionized ourunderstanding of the mechanism of ribosomal function andinhibition. Significant efforts have been made in trying toderivatize existing drugs to improve the interactions at theirbinding site, which is illustrated by the macrolide drugs andketolide derivatives. 9 - 11 The crystal structures 12 - 15 of ribosome - SPS complex capture the binding mode of SPS in the presenceof P-site tRNA and support to some extent the hypothesissuggested from the earlier biochemical and kinetic studies. 16 - 20 Despite the extensive experimental investigations, the energeticdriving forces for the ribosome - antibiotic interaction are stillnot clear.Computations based on atomic models can help shed somelight on these issues. Alchemical free energy perturbationmolecular dynamics (FEP/MD) simulations, in particular, is apowerful approach to study the ligand - macromolecule associa-tion processes at the atomic level 21 - 26 (for recent reviews, seerefs 27 and 28). However, calculation of the absolute bindingfree energy of antibiotics to the ribosome encounters extremechallenges due to the large size of the ribosomal target, hydrationof the buried binding pocket, conformational flexibility of theligands, and the interaction with counterions. These factors alsoincrease the difficulties to accurately predict the binding affinityof antibiotics to the ribosome with scoring functions intraditional docking approaches. 29 - 32 For these reasons, fewcomputational studies have been reported to date on investiga-tion of small-molecule binding to the ribosome, 33 - 35 especiallyfor the large subunit as a target. 36 The present study is aimed at clarifying the microscopicinteractions responsible for the binding of SPS analogs to theribosome. A set of SPS derivatives (Figure 1), created bychemical modifications, is used as probes to study the mecha-nism of ribosome - antibiotic interaction based on the atomicresolution structure of ribosome - SPS complex. The standardbinding free energies are calculated using FEP/MD simulations * Corresponding author. E-mail: roux@uchicago.edu. † Weill Medical College of Cornell University. ‡ The University of Chicago. § Argonne National Laboratory.  J. Phys. Chem. B  2010,  114,  9525–9539  9525 10.1021/jp100579y  ©  2010 American Chemical SocietyPublished on Web 07/07/2010  of a reduced system modeled via the generalized solventboundary potential (GSBP) method. 37 To enhance the samplingand facilitate the convergence of the FEP/MD calculations,restraining potentials acting on orientational, translational, andconformational freedom of the ligand and receptor are appliedand their biasing effects are removed rigorously. To accountfor the fluctuation in the number of water molecules in thedeeply buried pocket of the ribosome P-site during the perturba-tion, a grand canonical Monte Carlo (GCMC) algorithm isincorporated into the FEP/MD simulation protocol. 38 To ef-ficiently sample the conformational changes of ligands uponbinding, we used a method based on the potential of mean force(PMF) of the ligand as a function of the root-mean-squaredeviation (rmsd) relative to its bound conformation. This FEP/ MD strategy based on restraining potentials and PMF was firstintroduced to treat the binding of phosphotyrosine peptide toSH2 domain. 39 In the following, the theory and computational methodologiesare presented. The results from the free energy study are thendescribed and discussed. Finally, the article is concluded with asummaryofthekeyissuesaddressedinthisworkandtheremainingchallenges in binding free energy scoring of ribosomal drugs. Theory and Methods The present computations were carried out according to themethods described in Ge and Roux. 40 The FEP/MD simulationsare based on a protocol with restraining potentials that waselaborated previously 22,23 and which is an extension of thealchemical FEP/MD simulation approach called double-decou-pling method (DDM) 41 (see also ref 42). In classical statisticalmechanics, the microscopic term equilibrium constant  K  b  canbe expressed as 23 where  U   is the total potential energy of the system,  L  and  X are the coordinates of the ligand and the remaining atoms(solvent and receptor), respectively,  k  B  is the Boltzmannconstant,  T   is the temperature,  r L  is the position of the masscenter of the ligand, and  r * is some arbitrary location in thebulk region. 23,39,43 The delta function  δ ( r L  -  r *) in thedenominator arises from the translational invariance of ligandin the bulk volume. Hence  K  b  has the dimension of volume(Å 3 ). By multiplying with the standard concentration  C  o of 1mol/L (1/1660 Å 3 ), one can define a meaningful binding freeenergy ∆ G bo )- k  B T   ln( C  o K  b ). The standard binding free energyobtained from the stepwise transformations can be expressedaswhere  ∆∆ G int  )  [ ∆ G intsite -  ∆ G intbulk ] is the contribution fromnonbonded molecular interactions between the ligand and itssurrounding, and  ∆∆ G c  )  [ ∆ G cbulk -  ∆ G csite ],  ∆∆ G r  )  [ - k  B T  ln ( F  r )  -  ∆ G rsite ], and  ∆∆ G t °  )  [ - k  B T   ln( F  t C  o )  -  ∆ G tsite ] arethe contributions from the loss of conformational, orientational,and translational freedom of the ligand upon binding, respec-tively. The standard concentration  C  o cancels the Å 3 units of  F  t .This formulation decomposes the binding free energy intocontributions from individual factors. Although the values of the contributions depend on the details of the restraint potentials,the total standard binding free energy is rigorously independentof the restraints. The free energy components provide insightson what drives the binding process. 22,44 Intuitively, the ligandconformational contribution ∆∆ G c  and the ligand translationaland rotational contributions ( ∆∆ G r  +  ∆∆ G t ° ) are alwayspositive, disfavoring the binding reaction. The free energydecomposition might also be helpful to clarify the significanceof approximations such as the linear interaction energy (LIE) 45,46 and the molecular mechanics Poisson - Boltzmann solvent area(MM-PBSA), 47 - 49 although more elaborate theoretical develop-ments would be required to establish a formal derivation of thosetreatments.To gain more insight, we separate the nonbonded intermo-lecular forces into three major contributions: the short-range Figure 1.  Structures of SPS and its analogs modeled for the free energy calculations. K  b  ) ∫ site d L ∫ d X e - U   /  k  B T  ∫ bulk d L  δ ( r L  -  r *) ∫ d X  e - U   /  k  B T  (1) ∆ G b o )  ∆∆ G int  +  ∆∆ G t o +  ∆∆ G r  +  ∆∆ G c  (2) 9526  J. Phys. Chem. B, Vol. 114, No. 29, 2010  Ge and Roux  harsh repulsive interactions, slowly varying van der Waalsattraction and electrostatic interactions. A staged decoupling FEPscheme based on the Weeks - Chandler - Andersen (WCA) 50 separation of the Lennard-Jones (LJ) 12-6 potential waspioneered by Deng and Roux. 51 The WCA decoupling schemeprovides a clear conceptual separation of the competingrepulsive and dispersive forces in the solvation process andgreatly enhances the efficiency of solvation free energy com-putations and helps construct a robust and efficient method forcalculating binding free energies. It has proven useful in anumber of subsequent studies. 52,53 On the basis of the step-by-step reversible work, the interaction free energy can bedecomposed into three components,where ∆∆ G rep ) [ ∆ G repsite - ∆ G repbulk ], ∆∆ G dis ) [ ∆ G dissite - ∆ G disbulk ],and ∆∆ G elec ) [ ∆ G elecsite - ∆ G elecbulk ] correspond to the free energycontributions in terms of repulsion (rep), dispersion (dis), andelectrostatics (elec), respectively.Binding reactions usually occur at the expense of entropy,which includes the loss of translational, orientational, andconformational freedom for both the ligand and the receptor.The translational and rotational free energy contributions areusually computed by introducing a coupling parameter thatcontrols the strength of restraining potentials. The conforma-tional contributions for the bound and free ligand are determinedin two steps. During the FEP/MD calculations, the ligand isrestrained to remain near a reference conformation using abiasing potential. The restraining potential is a quadraticpotential,  u c  )  k  c ξ 2 , where  ξ  is the rmsd of the ligand relativeto its bound conformation, used as a reference. The free energiesassociated with the conformational restriction of the ligand ∆ G cbulk and  ∆ G csite , are calculated by by explicitly integratingthe Boltzmann factor of the PMFs,andwhere  W  cbulk ( ξ ) and  W  csite ( ξ ) are the PMFs of the ligand in thebulk and the binding site, respectively. The explicit integrationof the Boltzmann-weighted PMF in eqs 4 and 5 is a generalprocedure that rigorously removes the bias of the conformationalrestraining potential  u c . The PMF as a function of rmsd iscalculated from umbrella sampling simulations generated witha biasing potential centered on successive values of rmsdoffset. 39 Computational DetailsStructural Models for the Bound SPS Analogs.  The crystalstructure of SPS bound ribosome 50S complex (PDB code1M90) 6 was used as the template for the analog-boundcomplexes. The topology of CCA-Phe-caproic acid (CAP) wasgenerated by linking the N-terminal of Phe-CAP to the 3 ′  endof CCA using the PATCH command of CHARMM. 54 Hydrogenatoms were added using the HBUILD 55 facility in CHARMM. 54 The initial configurations of the bound analogs were built bymodifying the functional groups on the bound SPS using theVMD program. 56 The structures of the SPS analogs are shownin Figure 1. Each complex structure contains about 150 000atoms excluding waters.The CHARMM27 force field was used for the ribosomestructure, including RNA, protein, and ion species. 57,58 TheTIP3P water model was used. 59 The generalized AMBER forcefield (GAFF) was used for all the SPS analogs. 60,61 In general,different molecular mechanical force fields are not necessarilycompatible, and this should be done with caution. However, inthe present case the two force fields share a similar functionalform, and both were developed to be consistent with the TIP3Pwater model. In addition, no apparent problems were noted inprevious studies of ligand binding and solvation following thisprocedure. 22,23,52 The topology and parameters (GAFF) of the ligands were generated in CHARMM format withANTECHAMER1.27. 60,61 The free ligands were optimized withGaussian 03 62 at B3LYP level with the aug-cc-pVDZ basisset. 63 - 65 Restrained electrostatic potential (RESP) 66 charges wereassigned as the atomic partial charges for the SPS analogs usingthe FitCharge module 67 of CHARMM, 54 obtained by optimizingthe charge fitting to QM electrostatic potential (ESP) maps.The GSBP method was used to generate a reduced simulationsystem of the ligands bound to the ribosome. A spherical innerregion of 15 Å radius from the center of the binding site wasused for all the analog ligands. The reduced systems comprise ∼ 4100 atoms. All the atoms including those of the ribosome,ligand, and solvent within the inner region are allowed to moveand fluctuate during the FEP/MD simulations. The inner regionwas extended by 3 Å to define a smooth spherical dielectriccavity. The ribosome atoms located in the 3 Å shell, and thosewithin the extended inner spherical region ( e 18 Å) linked via1 - 3 bonds with the outer region ( > 18 Å) were fixed accordingto a group-based criterion. In GSBP, the long-range electrostaticinfluence from the surrounding outer region on the atoms of the inner region is represented in terms of a solvent-shieldedstatic field and a solvent-induced reaction field. In addition, anonpolar cavity potential is present to keep the water moleculesinside the inner region. The reaction field due to the variationof charge distribution in the dynamic inner region is expressedin terms of a generalized multipolar expansion of the chargedistribution of the inner region. The basis set coefficientscorrespond to the generalized electrostatic multipoles and 9spherical harmonic functions were used for the ribosome - ligandcomplexes. In the generalized multiple calculation, all thecharges of the inner region are included. The solvent-shieldedstatic field and the reaction field matrix, representing thecouplings between the generalized multipoles, were calculatedonce with finite-difference Poisson - Bolztmann (PB), assumingdielectric constants of 4 inside the ribosome and 80 outside.Atomic Born radii for proteins, RNAs, and ions were calculatedfrom average solvent electrostatic charge distribution withexplicit solvent. 68,69 To match the physiological conditions, asalt concentration of 0.2 M was used for all the systems. Thetruncation of the Lennard-Jones interactions in the free energycalculation with GSBP also need to be considered; therefore, along-range correction for the van der Waals interactions of theligand with the rest of the system was estimated from an energycalculations using a cutoff of 30 Å. The solvent-shielded staticfield and the reaction field matrix are invariant with respect tothe configuration of the explicit atoms in the inner region. ∆∆ G int  )  ∆∆ G rep  +  ∆∆ G dis  +  ∆∆ G elec  (3) ∆ G cbulk ) - k  B T  ln ( ∫ d ξ  e - W  cbulk ( ξ )/  k  B T  e - u c ( ξ )/  k  B T  ∫ d ξ  e - W  cbulk ( ξ )/  k  B T  )  (4) ∆ G csite ) - k  B T   ln ( ∫ d ξ  e - W  csite ( ξ )/  k  B T  e - u c ( ξ )/  k  B T  ∫ d ξ  e - W  csite ( ξ )/  k  B T  )  (5) Free Energy Calculations of Sparsomycin Analogs  J. Phys. Chem. B, Vol. 114, No. 29, 2010  9527  Specifically, the GSBP setup is independent of the ligand boundin the inner region, the static field and the reaction field matrixpreviously calculated for SPS were therefore used for SPSanalogs in complex with ribosome.Nine Mg 2 + counterions were added to neutralize the phos-phate groups in the inner simulation region. The electrostaticinteractions between explicit atoms were included within thesimulation sphere and the interactions beyond 12 Å wererepresented using an extended electrostatic method. The GSBPsystems were hydrated with 20 cycles of MC and MD (10 000MC move followed by 10 000 MD steps with 2 fs time step).As previously, a weak harmonic restraint was applied onribosome nonhydrogen atoms throughout the simulations usinga force constant of 1 (kcal/mol)/Å 2 . 40 All bonds involvinghydrogen atoms were fixed with the SHAKE algorithm. TheMC steps included rigid body translation, rotation, and GCMCinsertion/deletion of water molecules, 38 attempted with equalprobability. The solvated ribosome - SPS analog complexes wereequilibrated for 3 ns at 300 K using Langevin dynamics with 2fs time step. A friction coefficient of 5 ps - 1 was assigned to allnonhydrogen atoms to ensure thermalization. To define thetranslational and rotational restraints for FEP calculation,the anchor atoms were selected randomly on the ribosome andthe ligands. The average of the last 1 ns MD trajectories werecalculated as the references for distance, angle, and dihedralrestraint parameters. The minimized average structures of boundligands were calculated from the last 1 ns MD trajectory andused as reference structures in the conformational restrainingpotential. The equilibrated systems for the different analogs areshown in Figure 2.The SPS analogs in bulk solvent were simulated using thespherical solvent boundary potential (SSBP) method. 70 A sphereof 1000 explicit water molecules was centered on each ligand.The systems were equilibrated for 200 ps at 300 K usingLangevin dynamics with 2 fs time step. A friction coefficientof 5 ps - 1 was assigned to all nonhydrogen atoms. FEP and PMF Calculations.  The FEP/MD simulations forthe five analogs were carried out with CHARMM versionc35a1. 54 The simulations in the binding site consist of 18windows of ligand repulsion, five windows of ligand dispersion,10 windows of ligand electrostatics, and 15 windows of restraints removal. Two set of trajectories (forward and back-ward perturbation) were generated for each window. Forrepulsion, dispersion, and electrostatics three stages, eachtrajectory consists of 6 cycles of a GCMC/MD run (10 000 MCsteps followed by MD with 10 ps equilibration and 10 ps datacollection). A further 20 ps MD and 10 ps data collection wasdone after the GCMC/MD cycles (for a total sampling time of 140 ps in each window). For the translational/rotational restraintpotential, each trajectory samples 140 ps starting from variousinitial velocities with series of coupling parameters (Table 1).The last 100 ps were collected and processed with the weightedhistogram analysis method (WHAM). 71,72 In the bulk solvent,the coupling parameters in repulsion, dispersion, and electrostat-ics stages were the same as for the bound ligand simulations.For the interaction contribution to the binding free energy, thelength of each window simulation was 70 ps equilibrationfollowed by 70 ps of sampling (140 ps in total for each window).All MD simulations were carried out using Langevin dynam-ics at 300 K with a friction constant corresponding to a Figure 2.  Equilibrated conformations of SPS and its analogs in the ribosomal binding site. Ribosome non-hydrogen atoms are represented bygreen lines. All the ligands are represented by thick sticks in CPK. Residue A2637 is represented by thin sticks, Mg118 is represented by greenspheres. Mg7 is represented by magenta spheres. Waters and backbone oxygens of RNA within 3 Å radius from Mg118 or Mg7 are representedby balls and sticks in CPK. Starting (gray) and equilibrated (light green) conformations are superimposed for (A) ribosome - SPS complex, (B)ribosome - AN1 complex, (C) ribosome - AN2 complex, (D) ribosome - AN3 complex, (E) ribosome - AN4 complex, and (F) ribosome - AN5 complex. TABLE 1: Values of the Coupling Parameters in the FEP Calculations  λ rep  0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0  λ dis  0.0 0.25 0.5 0.75 1.0  λ elec  0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0  λ t,r  0.0 0.003 0.005 0.007 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 9528  J. Phys. Chem. B, Vol. 114, No. 29, 2010  Ge and Roux  relaxation time of 5 ps applied to the nonhydrogen atoms. Thewater geometry was kept fixed using SHAKE, and the integra-tion time step was 2 fs. No cutoff was applied for the innerregion electrostatic interactions, but all electrostatic interactionsbeyond 12 Å were treated on the basis of dipolar andquadrupolar expansions using the extended electrostatic method.This reduced the computational time of the calculation by abouta factor of 2 relative to an infinite cutoff scheme.The free energies associated with the conformational restric-tion of the ligand near the reference conformation werecalculated by integration of the Boltzmann factor of the rmsdpotential of mean force (PMF) obtained from umbrella samplingsimulations. Twenty-one biasing windows were used with thermsd offset values increasing from 0.0 to 5.0 Å in steps of 0.25Å for the ligand in the binding site and in the bulk solution.For a more rapid convergence, the initial configurations for the21 umbrella sampling windows were generated using a shortinitial run with a strong force constant of 500 (kcal/mol)/Å 2 . Ineach window, the system was equilibrated using a force constantof 10 (kcal/mol)/Å 2 , and after 100 ps equilibration, a 400 pssimulation was used for sampling. To ensure the convergenceof the PMF calculations, 10 successive runs of umbrellasampling simulations (400 ps per window for each) wereconducted. No translational or orientational restraining potentialwas present during those simulations. The WHAM was usedto unbias the results and compute the PMF as a function of rmsd.The symmetric groups on the tails of ligands AN1 and AN3could undergo isomerization and interconversion betweenphysically equivalent conformations. It is computational de-manding to sample all the isomers in the binding site. Insufficientsampling of one state of the system over another during thethermodynamic decoupling would undermine an accurate esti-mate of the loss of conformational freedom upon ligand binding.To avoid this problem, a steep flat-bottom dihedral restrainingpotential was applied to all the symmetric units of the ligands,namely, the phenyl group on AN1 and the benzyl group on AN3.The restraint with a force constant of 500 (kcal/mol)/Å 2 wasapplied to the ligands during all the calculations in the bulk orthe binding site involving the conformational restrainingpotential, without affecting the physical property of the ligandand the final binding free energy. Results and Discussion The calculated standard binding free energies with theindividual energy components are given in Table 2 for SPS andits analogs. Experimental estimates of the dissociation constants K  D  obtained from affinity labeling experiments in the  E. coli strain vary from mM to  µ M; 18 thus, ∆ G bo ranges from about - 3to - 8 kcal/mol. The calculated binding free energy spans from + 2.34 to  - 7.94 kcal/mol. As shown in Figure 3A, the resultsfrom the computation have a good linear correlation with theexperimental data (  R 2 ) 0.96), although the slope (1.91) is largerthan 1.0, and the calculated values are systematically higherthan the experimental ones. For the strong binders, such as SPS,AN1, and AN3, the errors of computed versus experimental ∆ G bo range from 0.34 to 2.03 kcal/mol. In contrast, the errorsfor the weak binders like AN2, AN4, and AN5 can be as largeas 5 kcal/mol. A plausible explanation might be that imperfec-tions with the initial pose for the weak binders, leading tounderestimated affinity. There are also perhaps additionaldifficulties on the experimental side to measure weak affinitiesaccurately. Nevertheless, the inaccuracies with the weak bindersdo not affect the ranking of the six ligands, which is in excellentagreement with experiments.To ascertain the convergence of the FEP/MD calculation, aseries of ten free energy runs were carried out for each of theanalog ligands. Each new run was restarted by using the set of last configurations taken from the previous run (for all thecorresponding windows). As shown in Figure 4, the resultsapproach a stable value after a few cycles for all the solvationand binding free energy calculations. For all the ligands, thesimulations for the bulk phase converge rapidly after three runs.However, the simulations in the binding site typically appearto converge only after five runs. Therefore, the last five FEP/ MD runs (out of ten) were used to calculate the values in Table2. The slowest converging ligand is AN1 (blue line in Figure4A), which displays a drift up to runs 7 - 10. The configurationof this ligand seems to be very stable according to Figure 5, TABLE 2: Values of the Binding Free Energy of SPS Analogs with the Ribosome ligand system  ∆ G rep  ∆ G dis  ∆ G elec  ∆ G int  ∆ G t  +  ∆ G r  ∆ G c  ∆ G bo exptSPS site 71.21 ( 1.33  - 81.65 ( 0.17  - 58.60 ( 0.34  - 69.05 ( 1.20 1.65 ( 0.02 3.12bulk 34.33 ( 0.12  - 40.70 ( 0.16  - 40.41 ( 0.17  - 46.78 ( 0.19 6.64 + 6.38 8.17 ∆∆ G  36.88 ( 1.45  - 40.95 ( 0.33  - 18.19 ( 0.51  - 22.27 ( 1.39 11.37 ( 0.02 5.05  - 5.84 ( 1.37  - 7.87 ( 0.11AN1 site 74.88 ( 1.87  - 87.22 ( 0.12  - 50.35 ( 0.40  - 62.68 ( 1.99 2.22 ( 0.04 1.22bulk 35.12 ( 0.25  - 43.52 ( 0.35  - 33.02 ( 0.09  - 41.42 ( 0.34 7.12 + 6.16 3.48 ∆∆ G  39.76 ( 2.12  - 43.70 ( 0.47  - 17.33 ( 0.49  - 21.26 ( 2.33 11.06 ( 0.04 2.26  - 7.94 ( 2.32  - 8.28 ( 0.11AN2 site 62.60 ( 1.68  - 89.11 ( 0.29  - 32.39 ( 0.29  - 58.90 ( 1.61 1.57 ( 0.01 0.83bulk 35.90 ( 0.17  - 44.09 ( 0.25  - 34.38 ( 0.17  - 42.56 ( 0.37 6.98 + 6.20 6.02 ∆∆ G  26.70 ( 1.85  - 45.02 ( 0.54 2.01 ( 0.46  - 16.34 ( 1.98 11.61 ( 0.01 5.19  0.46 ( 1.99  - 4.12 ( 0.11AN3 site 87.26 ( 1.39  - 104.21 ( 0.08  - 48.99 ( 0.28  - 65.94 ( 1.38 3.74 ( 0.03 0.68bulk 42.26 ( 0.32  - 52.76 ( 0.27  - 35.05 ( 0.12  - 45.55 ( 0.37 7.05 + 6.35 8.36 ∆∆ G  45.00 ( 1.71  - 51.45 ( 0.35  - 13.94 ( 0.40  - 20.39 ( 1.75 9.66 ( 0.03 7.68  - 3.42 ( 1.78  - 4.85 ( 0.11AN4 site 69.50 ( 0.96  - 85.18 ( 0.28  - 33.35 ( 0.35  - 49.03 ( 1.04 1.88 ( 0.02 0.85bulk 35.46 ( 0.47  - 42.77 ( 0.33  - 27.13 ( 0.22  - 34.44 ( 0.50 6.94 + 6.73 5.96 ∆∆ G  34.04 ( 1.43  - 42.41 ( 0.61  - 6.22 ( 0.57  - 14.59 ( 1.54 11.79 ( 0.02 5.11  2.32 ( 1.53  - 3.52 ( 0.11AN5 site 62.89 ( 1.11  - 80.80 ( 0.27  - 39.42 ( 0.46  - 57.33 ( 1.13 1.33 ( 0.06 1.59bulk 37.30 ( 0.45  - 44.23 ( 0.11  - 38.06 ( 0.05  - 44.98 ( 0.44 5.84 + 6.58 5.19 ∆∆ G  25.59 ( 1.56  - 36.57 ( 0.38  - 1.36 ( 0.51  - 12.35 ( 1.57 11.09 ( 0.06 3.60  2.34 ( 1.54  - 3.35 ( 0.11Free energies in kcal/mol. The free energies for the site and the bulk are computed with the method described in ref 40. The errors of all thefree energy values except for  ∆ G c  are the standard deviation of the last five continuous simulation runs, each starting at random velocities withthe last configuration of the previous run. As an exception, the final results and errors for AN1 are calculated on the basis of the last four runs,due to the delay of steady state (Figure 4A). For conformational free energy  ∆ G c , the values are calculated on the basis of 3.6 ns PMFsimulation (run 2 - 10). All the errors of individial free energy  ∆ G  are unbiased RMS errors. Free Energy Calculations of Sparsomycin Analogs  J. Phys. Chem. B, Vol. 114, No. 29, 2010  9529
Search
Similar documents
View more...
Tags
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks