A method for conformational sampling of loops in proteins based on adiabatic decoupling and temperature or force scaling

A method for conformational Boltzmann sampling of loops in proteins in aqueous solution is presented that is based on adiabatic decoupling molecular dynamics (MD) simulation with temperature or force scaling. To illustrate the enhanced sampling, the loop from residues 33 to 43 in the bovine protein ribonuclease A is adiabatically decoupled from the rest of the protein and the solvent with a mass scaling factor s(m) =1000 and the sampling is enhanced with a scaling of the temperature using s(T) =2 or of the force using s(V) =0.667. Over 5 ns of simulation the secondary structure of the protein remains unaltered while a combined dihedral-angle conformational cluster analysis shows an increase of conformations outside the first most populated cluster of loop conformations for adiabatic decoupling MD with temperature scaling using s(T) =2 or force scaling using s(V) =0.667 compared to the standard MD simulation. The atom-positional root-mean-square fluctuations of the C(α) atoms of the loop show an increase in the movement of the loop as well, indicating that adiabatic decoupling MD with upscaling of the temperature or downscaling of the force is a promising method for conformational Boltzmann sampling.     

IR spectra of N-methylacetamide in water predicted by combined quantum mechanical/molecular mechanical molecular dynamics simulations

We applied the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulation method in assessing IR spectra of N-methylacetamide and its deuterated form in aqueous solutions. The model peptide is treated at the Austin Model 1 (AM1) level and the induced dipole effects by the solvent are incorporated in fluctuating solute dipole moments, which are calculated using partial charges from Mulliken population analyses without resorting to any available high-level ab initio dipole moment data. Fourier transform of the solute dipole autocorrelation function produces in silico IR spectra, in which the relative peak intensities and bandwidths of major amide bands are quantitatively compatible with experimental results only when both geometric and electronic polarizations of the peptide by the solvent are dealt with at the same quantum-mechanical level. We cast light on the importance of addressing dynamic charge fluctuations of the solute in calculating IR spectra by comparing classical and QM/MM MD simulation results. We propose the adjustable scaling factors for each amide mode to be directly compared with experimental data.     

Energy minimization and molecular dynamics studies of Asn-102 elastase

Summary Four isomeric forms of the Asn-102 PPE (D 102 N mutant according to the emerging protocol, [Knowles, Science, 236 (1987) 1252–1258]) have been investigated using energy minimization (EM) and molecular dynamics (MD) techniques. MD simulation data for 175 ps are reported for each form (in total 700 ps for about 2500 atoms). The His-57 N-protonated forms are calculated to be more stable than the N-protonated ones. The active site region of the most stable form is very similar to that found in the D102N rat trypsin enzyme [Craik et al., Science, 237 (1987) 909–913]. Conformations of the active sites and their hydrogen bond patterns are presented for each of these forms and are compared with the structure of the native enzyme active site. The pH dependent activity of the D102N derivative is discussed.     

Promiscuity in alkaline phosphatase superfamily. Unraveling evolution through molecular simulations

We here present a theoretical study of the alkaline hydrolysis of a phosphodiester (methyl p-nitrophenyl phosphate or MpNPP) in the active site of Escherichia coli alkaline phosphatase (AP), a monoesterase that also presents promiscuous activity as a diesterase. The analysis of our simulations, carried out by means of molecular dynamics (MD) simulations with hybrid quantum mechanics/molecular mechanics (QM/MM) potentials, shows that the reaction takes place through a D(N)A(N) or dissociative mechanism, the same mechanism employed by AP in the hydrolysis of monoesters. The promiscuous activity observed in this superfamily can be then explained on the basis of a conserved reaction mechanism. According to our simulations the specialization in the hydrolysis of phosphomonoesters or phosphodiesters, developed in different members of the superfamily, is a consequence of the interactions established between the protein and the oxygen atoms of the phosphate group and, in particular, with the oxygen atom that bears the additional alkyl group when the substrate is a diester. A water molecule, belonging to the coordination shell of the Mg(2+) ion, and residue Lys328 seem to play decisive roles stabilizing a phosphomonoester substrate, but the latter contributes to increase the energy barrier for the hydrolysis of phosphodiesters. Then, mutations affecting the nature or positioning of Lys328 lead to an increased diesterase activity in AP. Finally, the capacity of this enzymatic family to catalyze the reaction of phosphoesters having different leaving groups, or substrate promiscuity, is explained by the ability of the enzyme to stabilize different charge distributions in the leaving group using different interactions involving either one of the zinc centers or residues placed on the outer side of the catalytic site.     

New force field for calcium binding sites in annexin-membrane complexes

For accurate classical molecular dynamics (MD) simulations of the calcium mediated bound complexes of annexin and membrane we have developed new force-field parameters correctly describing the interaction of the Ca ion with its environment. We have used quantum chemical calculations to investigate the potential energy surface experienced by the Ca ion within the three different binding sites found in domain 1 of annexin V (ANX V/1). Based on these calculations we were able to quantify the charge polarization of atoms within the binding sites, and to determine the geometry and force constants of harmonic restraints between the Ca ion and its coordinating oxygen atoms. Harmonic restraints were introduced to compensate for the deviations between the quantum mechanical potential energy surface and that of the classical force field. Our analysis has shown that using the refined force field for the Ca binding sites enables long-time MD simulations that conserve the initial structure of ANX V/1 significantly better than MD simulations using the standard force field.     

Simulated scaling method for localized enhanced sampling and simultaneous "alchemical" free energy simulations: a general method for molecular mechanical, quantum mechanical, and quantum mechanical/molecular mechanical simulations

A potential scaling version of simulated tempering is presented to efficiently sample configuration space in a localized region. The present "simulated scaling" method is developed with a Wang-Landau type of updating scheme in order to quickly flatten the distributions in the scaling parameter lambdam space. This proposal is meaningful for a broad range of biophysical problems, in which localized sampling is required. Besides its superior capability and robustness in localized conformational sampling, this simulated scaling method can also naturally lead to efficient "alchemical" free energy predictions when dual-topology alchemical hybrid potential is applied; thereby simultaneously, both of the chemically and conformationally distinct portions of two end point chemical states can be efficiently sampled. As demonstrated in this work, the present method is also feasible for the quantum mechanical and quantum mechanical/molecular mechanical simulations.     

Toward a new approach for determination of solute's charge distribution to analyze interatomic electrostatic interactions in quantum mechanical/molecular mechanical simulations

We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods.     

高能混合物的感度理论判别—— 不同配比和不同温度AP/HMX的MD研究

为了寻求高能复合材料的感度理论判据, 对高氯酸铵(AP)和HMX(环四甲撑四硝胺)所构成的不同质量比的二元混合体系, 用分子动力学(MD)方法和修正的PCFF力场, 作正则系综(NVT)下的周期性模拟计算, 求得其结合能和HMX热解引发键(N—NO2)的平均键长和最大键长. 结果表明, 结合能随质量比不同呈复杂变化趋势; HMX(N—NO2)引发键的最大键长随体系中HMX配比增加先增后减, 而当AP/HMX为1∶1时其值最大, 恰与此配比下感度最大的实验事实相一致. 选择质量比为1∶1的AP/HMX作不同温度下的NVT-MD模拟, 发现引发键(N—NO2)最大键长随温度升高而递增, 与感度随温度升高而增大的实验事实相符. 为此我们建议, 把高能复合材料中易爆燃组分引发键的最大键长作为其热和撞击等感度的理论判据, 借以阐明、比较或预示它们的相对安全性.     

Probing the origin of the compromised catalysis of E. coli alkaline phosphatase in its promiscuous sulfatase reaction

The catalytic promiscuity of E. coli alkaline phosphatase (AP) and many other enzymes provides a unique opportunity to dissect the origin of enzymatic rate enhancements via a comparative approach. Here, we use kinetic isotope effects (KIEs) to explore the origin of the 109-fold greater catalytic proficiency by AP for phosphate monoester hydrolysis relative to sulfate monoester hydrolysis. The primary 18O KIEs for the leaving group oxygen atoms in the AP-catalyzed hydrolysis of p-nitrophenyl phosphate (pNPP) and p-nitrophenylsulfate (pNPS) decrease relative to the values observed for nonenzymatic hydrolysis reactions. Prior linear free energy relationship results suggest that the transition states for AP-catalyzed reactions of phosphate and sulfate esters are "loose" and indistinguishable from that in solution, suggesting that the decreased primary KIEs do not reflect a change in the nature of the transition state but rather a strong interaction of the leaving group oxygen atom with an active site Zn2+ ion. Furthermore, the primary KIEs for the two reactions are identical within error, suggesting that the differential catalysis of these reactions cannot be attributed to differential stabilization of the leaving group. In contrast, AP perturbs the KIE for the nonbridging oxygen atoms in the reaction of pNPP but not pNPS, suggesting a differential interaction with the transferred group in the transition state. These and prior results are consistent with a strong electrostatic interaction between the active site bimetallo Zn2+ cluster and one of the nonbridging oxygen atoms on the transferred group. We suggest that the lower charge density of this oxygen atom on a transferred sulfuryl group accounts for a large fraction of the decreased stabilization of the transition state for its reaction relative to phosphoryl transfer.     

Y:BaZrO3 Perovskite Compounds II: Designing Protonic Conduction by using MD Models

The proton dynamics in Y‐doped BaZrO₃ derivatives, in particular the different dopant environments within a Pm${\bar 3}$ m cubic framework, were studied by using classical molecular dynamics (MD) calculations. Single‐ and double substitution of zirconium by yttrium atoms was considered. The presence of yttrium induced variations in the surrounding oxygen sites, according to their local geometrical arrangements. The differences among such distinct oxygen sites became evident when protons interacted with them and upon changes in the temperature. So, different proton transfer pathways, which had different energy barriers, characterized the topologically different oxygen sites. The experimental proton‐hopping activation energy was only reproduced in those structures in which two yttrium atoms formed a Y‐O‐Y arrangement, which also acted as multilevel protonic traps. Protonic conduction in these materials could be improved by avoiding such yttrium clustering, hence preventing the formation of the protonic traps.     

Electronic spectra of adenine and 2-aminopurine: an ab initio study of energy level diagrams of different tautomers in gas phase and aqueous solution

Ground and lowest two singlet excited state geometries of four tautomeric forms (N9H, N7H, N3H and N1H) of each of adenine and 2-aminopurine (2AP) were optimized using an ab initio approach employing a mixed basis set (6-311 + G* on the nitrogen atom of the amino group and 4-31G basis set on the other atoms). Excited states were generated employing configuration interaction involving single electron excitations (CIS). Subsequently, the different species were solvated in water employing the self-consistent reaction field (SCRF) approach along with the corresponding gas phase optimized geometries. Thus the observed absorption and fluorescence spectra of adenine and 2AP have been explained successfully. It is concluded that both the N9H and N7H forms of 2AP would contribute to absorption and fluorescence spectra. Further, the fluorescence of 2AP would be absorbed by its cation in which both the N9 and N7 atoms are protonated, the fluorescence of which can have an anti-Stokes component. Among the different tautomers of adenine, the N9H form would be present dominantly in the ground state in aqueous solutions but the N7H form would be produced by energy transfer and subsequent fluorescence. The N3H form of adenine appears to be responsible for the observed absorption near 300 nm by its solutions intermittently exposed to ultraviolet radiation. The rings of the different species related to 2AP and adenine remain almost planar in the pi-pi* and n-pi* singlet excited states as in the ground state. The pyramidal character of the amino group is usually less in the pi-pi* excited states than that in the corresponding ground or n-pi* excited states. Molecular electrostatic potential (MEP) maps of the molecules provide useful clues regarding phototautomerism.     

Molecular dynamics study on the relationships of modeling, structural and energy properties with sensitivity for RDX-based PBXs

In this paper,a primary model is established for MD(molecular dynamics) simulation for the PBXs(polymer-bonded explosives) with RDX(cyclotrimethylene trinitramine) as base explosive and PS as polymer binder.A series of results from the MD simulation are compared between two PBX models,which are represented by PBX1 and PBX2,respectively,including one PS molecular chain having 46 repeating units and two PS molecular chains with each having 23 repeating units.It has been found that their structural,interaction energy and mechanical properties are basically consistent between the two models.A systematic MD study for the PBX2 is performed under NPT conditions at five different temperatures,i.e.,195 K,245 K,295 K,345 K,and 395 K.We have found that with the temperature increase,the maximum bond length(L max) of RDX N N trigger bond increases,and the interaction energy(E N-N) between two N atoms of the N-N trigger bond and the cohesive energy density(CED) decrease.These phenomena agree with the experimental fact that the PBX becomes more sensitive as the temperature increases.Therefore,we propose to use the maximum bond length L max of the trigger bond of the easily decomposed and exploded component and the interaction energy E N-N of the two relevant atoms as theoretical criteria to judge or predict the relative degree of heat and impact sensitivity for the energetic composites such as PBXs and solid propellants.     

Alkaline phosphatase catalysis is ultrasensitive to charge sequestered between the active site zinc ions

Escherichia coli alkaline phosphatase (AP) is a prototypical bimetalloenzyme, facilitating catalysis of phosphate monoester hydrolysis with two Zn2+ metal ions that are only 4 A apart. In the reaction's transition state, one of the nonbridging oxygen atoms of the transferred group appears to interact directly with the Zn2+ ion metallocluster. To determine the importance and the energetic properties of this interaction, we systematically varied the charge on this oxygen atom, exploiting the ability of AP to catalyze reactions of different classes of substrates. We observed that the AP catalytic proficiency correlates very well (R2 = 0.98) with the charge on this oxygen atom, over 8 orders of magnitude of catalytic proficiency. The slope of this linear correlation (31 +/- 2 kcal/mol per unit charge) is extraordinarily steep, indicating that AP greatly discriminates between differentially charged substrates. We suggest that this discrimination arises via an electrostatic interaction with the bimetallocluster. The dependence of the AP catalytic proficiency on the nonbridging oxygen charge is much larger than charge perturbation effects observed previously for other proteins. We propose that AP uses folding energy to position the two Zn2+ metal ions in close proximity, thereby creating an active site with a high electrostatic potential that is extraordinarily sensitive to the charge that "solvates" the metallocluster. The sensitivity of enzyme energetics to systematic variation in electrostatic properties provides a powerful measure of the active site environment. Future work comparing the sensitivity of related enzymes that have been optimized to catalyze different reactions will help reveal how natural selection has tuned related active sites to favor different reactions.     

Isomerization dynamics and thermodynamics of ionic argon clusters

The dynamics and thermodynamics of small Ar(n) (+) clusters, n=3, 6, and 9, are investigated using molecular dynamics (MD) and exchange Monte Carlo (MC) simulations. A diatomic-in-molecule Hamiltonian provides an accurate model for the electronic ground state potential energy surface. The microcanonical caloric curves calculated from MD and MC methods are shown to agree with each other, provided that the rigorous conservation of angular momentum is accounted for in the phase space density of the MC simulations. The previously proposed projective partition of the kinetic energy is used to assist MD simulations in interpreting the cluster dynamics in terms of inertial, internal, and external modes. The thermal behavior is correlated with the nature of the charged core in the cluster by computing a dedicated charge localization order parameter. We also perform systematic quenches to establish a connection with the various isomers. We find that the Ar(3) (+) cluster is very stable in its linear ground state geometry up to about 300 K, and then isomerizes to a T-shaped isomer in which a quasineutral atom lies around a charged dimer. In Ar(6) (+) and Ar(9) (+), the covalent trimer core is solvated by neutral atoms, and the weakly bound solvent shell melts at much lower energies, occasionally leading to a tetramer or pentamer core with weakly charged extremities. At high energies the core itself becomes metastable and the cluster transforms into Ar(2) (+) solvated by a fluid of neutral argon atoms.     

The interaction of hyperthermal nitrogen with N-covered Ag(111)

A mixed beam of hyperthermal N atoms and N(2) molecules was scattered from the N-covered Ag(111) surface held at 300 K. The angular distribution of scattered N atoms is very broad. In contrast, N(2) molecules exhibit a sharp angular distribution. Taking into account the relative mass ratio, N loses more energy at the surface than N(2). In terms of energy loss, the atoms approximately follow the binary collision model while the molecules do not. Instead, the energy curves of scattered N(2) are more comparable to the parallel momentum conservation model for near specular outgoing angles (40°-65°). For both atoms and molecules the angle-resolved intensity and final energy curves are very similar to those from the bare surface. However, the N-covered surface yields non-negligible N(2) intensity for a broad range of outgoing angles, including along the surface normal. This was not the case from the clean surface, where the measured intensity distribution was confined to the narrower angular range indicated above. Backscattering and direct abstraction reactions are evaluated as possible origins of this additional N(2) signal. Of these, an abstraction mechanism appears to be the most consistent with the measured data.     

Ionization dynamics of aminopyridine dimer: a direct ab initio molecular dynamics (MD) study

The ionization dynamics of an aminopyridine dimer (AP)(2) has been investigated by means of the direct ab initio molecular dynamics (MD) method. It was found that the reaction process was composed of three steps after the vertical ionization of (AP)(2): dimer approach, proton transfer and energy relaxation. The timescales of these processes were 50-100, 10-20, and 200 fs, respectively. The timescale of the dimer approach was dependent on the initial separation between AP(+) and AP. After the ionization, AP approached gradually the ionized AP(+). The proton of AP(+) was transferred to AP at the nearest intermolecular distance, while the potential energy was quickly dropped according to the proton transfer. The energy relaxation of the dimer cation was significantly faster than that of the monomer cation. The mechanism of ionization dynamics of (AP)(2) was discussed on the basis of the theoretical results.     

Theoretical investigation of CO interaction with copper sites in zeolites: periodic DFT and hybrid quantum mechanical/interatomic potential function study

Periodic DFT and combined quantum mechanics/interatomic potential function (QM-pot) models were used to describe the interaction of CO with the Cu+ sites in FER. The CO stretching frequencies were calculated using omega(CO)(CCSD(T))/r(CO)(DFT) scaling method relating frequencies determined using a high-level quantum-chemical (coupled clusters) method for simple model carbonyls to CO bond lengths calculated using periodic DFT and QM-pot methods for the Cu+-zeolite system. Both periodic DFT and QM-pot models together with omega(CO)/r(CO) scaling describe the CO stretching dynamics with the "near spectroscopic accuracy", giving nu(CO) = 2156 cm(-1) in excellent agreement with experimental data. Calculations for various Cu+ sites in FER show that both types of Cu+ sites in FER (channel-wall sites and intersection sites) have the same CO stretching frequencies. Thus, the CO stretching frequencies are not site-specific in the CO/Cu+/FER system. The convergence of the results with respect to the model size was analyzed. When the same exchange-correlation functional is used the adsorption energies from periodic DFT and QM-pot are in good agreement (about 2 kcal/mol difference) but substantially larger than those of the experiment. The adsorption energy calculated with the B3LYP functional agrees with available experimental data. The overestimation of the adsorption energy in DFT calculations (periodic or QM-pot) is related to a red-shift of the CO stretching mode, both result from an underestimation of the HOMO(5sigma)-LUMO(2pi) gap of CO and the consequent overestimation of the Cu(+)(d)-CO(2pi*) back-donation. For the adsorption energy, this can be overcome by the use of hybrid B3LYP exchange-correlation functional. For the frequency calculations, the DFT problem can be overcome by the use of the omega(CO)(CCSD(T))/r(CO)(DFT) correlation.     

Theoretical study on the interaction of sulfur‐ and aminopyridine‐containing chelating resins with Hg(II) and Pb(II)

The geometries and energetics of complexes of Hg(II) and Pb(II) with sulfur‐ and aminopyridine‐containing chelating resin including crosslinked polystyrene immobilizing 2‐aminopyridine via sulfur‐containing (PVBS‐AP), sulfoxide‐containing (PVBSO‐AP), and sulfone‐containing (PVBSO₂‐AP) spacer arms have been investigated theoretically, and thus interactions of the metal ions with chelating resins were evaluated. The results indicate that PVBS‐AP behaves as a tridentate ligand to coordinate with the metal ions by S and two N atoms to form chelating compounds with S atom playing a dominant role in the coordination, whereas PVBSO‐AP and PVBSO₂‐AP interact with metal cations, respectively, in a tricoordinate manner by O and two N atoms forming chelating complexes. Furthermore, it is revealed that O and N2 atoms of PVBSO‐AP are the main contributor of coordination to Hg(II), whereas N2 atom of PVBSO₂‐AP is mainly responsible for the coordination to Hg(II). For PVBSO‐AP‐Pb²⁺ and PVBSO₂‐AP‐Pb²⁺ complex, the coordination is dominated by the synergetic effect of N1, N2, and O atoms. Natural bond orbital and second‐order perturbation analyses suggest that the charge transfer from the chelating resins to metal ions is mainly dominated by the interactions of lone pair of electrons of the donor atoms with the unoccupied orbitals of metal ions. Hg(II) complexes exhibit larger binding energies than the corresponding Pb(II) complexes, implying the chelating resins exhibit higher affinity toward Hg(II), which is consistent with the experimental results. Combined the theoretical and experimental results, further understanding of the structural information of the complexes and the coordination mechanism was achieved. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Promoting vibrations in human purine nucleoside phosphorylase. A molecular dynamics and hybrid quantum mechanical/molecular mechanical study

Crystallographic studies of human purine nucleoside phosphorylase (hPNP) with several transition-state (TS) analogues in the immucillin family showed an unusual geometric arrangement of the atoms O-5', O-4', and O(P), the nucleophilic phosphate oxygen, lying in a close three-oxygen stack. These observations were corroborated by extensive experimental kinetic isotope effect analysis. We propose that protein-facilitated dynamic modes in hPNP cause this stack, centered on the ribosyl O-4' oxygen, to squeeze together and push electrons toward the purine ring, stabilizing the oxacarbenium character of the TS. As the N-ribosidic bond is cleaved during the reaction, the pK(a) values of N-7 and O-6 increase by the electron density expelled by the oxygen-stack compression toward the purine ring. Increased electron density in the purine ring improves electrostatic interactions with nearby residues and facilitates the abstraction of a proton from a solvent proton or an unidentified general acid, making the purine a better leaving group, and accelerating catalysis. Classical and mixed quantum/classical molecular dynamics (MD) simulations of the Michaelis complex of hPNP with the substrates guanosine and phosphate were performed to assess the existence of protein-promoting vibrations (PPVs). Analogous simulations were performed for the substrates in aqueous solution. In the catalytic site, the O-5', O-4', and O(P) oxygens vibrate at frequencies of ca. 125 and 465 cm(-1), as opposed to 285 cm(-1) in the absence of hPNP. The hybrid quantum mechanical/molecular mechanical method was used to assess whether this enzymatic vibration pushing the oxygens together is coupled to the reaction coordinate, and thus has a direct positive impact on catalysis. The potential energy surface for the phosphorolysis reaction for several snapshots taken from the classical MD simulation showed substantial differences in oxygen compression. Our calculations showed the existence of PPVs coupled to the reaction coordinate, which effect electronic alterations in the active site by pushing the three oxygen centers together in proximity, and accelerate substrate turnover in the phosphorolysis reaction catalyzed by hPNP.     

Increasing the time step with mass scaling in Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations

Born‐Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state‐of‐the‐art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass‐scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass‐scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009