Influence of variation of a side chain on the folding equilibrium of a β‐peptide: Limitations of one‐step perturbation

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94 , 597), the one‐step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔG_F,U of six hepta‐β‐peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔG_F,U values obtained using one‐step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft‐core atoms in the side chain of the fifth residue showed an overall accuracy of about k_BT for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference‐state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ₁ and χ₂ torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔG_F,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one‐step perturbation technique to compute free enthalpies of folding are discussed. © 2013 Wiley Periodicals, Inc.     

Molecular dynamics simulations and free energy calculations on the enzyme 4‐hydroxyphenylpyruvate dioxygenase

4‐Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one‐step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Using one‐step perturbation to predict the effect of changing force‐field parameters on the simulated folding equilibrium of a β‐peptide in solution

Computer simulation using molecular dynamics is increasingly used to simulate the folding equilibria of peptides and small proteins. Yet, the quality of the obtained results depends largely on the quality of the force field used. This comprises the solute as well as the solvent model and their energetic and entropic compatibility. It is, however, computational very expensive to perform test simulations for each combination of force‐field parameters. Here, we use the one‐step perturbation technique to predict the change of the free enthalpy of folding of a β‐peptide in methanol solution due to changing a variety of force‐field parameters. The results show that changing the solute backbone partial charges affects the folding equilibrium, whereas this is relatively insensitive to changes in the force constants of the torsional energy terms of the force field. Extending the cut‐off distance for nonbonded interactions beyond 1.4 nm does not affect the folding equilibrium. The same result is found for a change of the reaction‐field permittivity for methanol from 17.7 to 30. The results are not sensitive to the criterion, e.g., atom‐positional RMSD or number of hydrogen bonds, that is used to distinguish folded and unfolded conformations. Control simulations with perturbed Hamiltonians followed by backward one‐step perturbation indicated that quite large perturbations still yield reliable results. Yet, perturbing all solvent molecules showed where the limitations of the one‐step perturbation technique are met. The evaluated methodology constitutes an efficient tool in force‐field development for molecular simulation by reducing the number of required separate simulations by orders of magnitude. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Single-step perturbations to calculate free energy differences from unphysical reference states: limits on size,flexibility, and character

Relative free energies for a series of not too different compounds can be estimated accurately from a single simulation of an unphysical reference state that encompasses the characteristic molecular features of the compounds. Previously, this method has been applied to the calculation of free energies of solvation and of ligand binding for small molecules. In the present study we investigate the limits to the accuracy of the method by applying it to a realistic model of the binding of a set of rather large ligands to the protein factor Xa, a key protein in current efforts to design anticoagulation drugs. The evaluation of the binding free energies and conformations of nine derivatives of a biphenylamidino inhibitor leads to insights regarding the effect of the size, flexibility, and character of the unphysical part of the ligand in the reference state on the accuracy of the predicted binding free energies.     

Multi‐state multi‐reference Møller–Plesset second‐order perturbation theory for molecular calculations

This work presents multi‐state multi‐reference Møller–Plesset second‐order perturbation theory as a variant of multi‐reference perturbation theory to treat electron correlation in molecules. An effective Hamiltonian is constructed from the first‐order wave operator to treat several strongly interacting electronic states simultaneously. The wave operator is obtained by solving the generalized Bloch equation within the first‐order interaction space using a multi‐partitioning of the Hamiltonian based on multi‐reference Møller–Plesset second‐order perturbation theory. The corresponding zeroth‐order Hamiltonians are nondiagonal. To reduce the computational effort that arises from the nondiagonal generalized Fock operator, a selection procedure is used that divides the configurations of the first‐order interaction space into two sets based on the strength of the interaction with the reference space. In the weaker interacting set, only the projected diagonal part of the zeroth‐order Hamiltonian is taken into account. The justification of the approach is demonstrated in two examples: the mixing of valence Rydberg states in ethylene, and the avoided crossing of neutral and ionic potential curves in LiF. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Free‐energy calculations of residue mutations in a tripeptide using various methods to overcome inefficient sampling

Previous free‐energy calculations have shown that the seemingly simple transformation of the tripeptide KXK to KGK in water holds some unobvious challenges concerning the convergence of the forward and backward thermodynamic integration processes (i.e., hysteresis). In the current study, the central residue X was either alanine, serine, glutamic acid, lysine, phenylalanine, or tyrosine. Interestingly, the transformation from alanine to glycine yielded the highest hysteresis in relation to the extent of the chemical change of the side chain. The reason for that could be attributed to poor sampling of φ₂/ψ₂ dihedral angles along the transformation. Altering the nature of alanine's C_β atom drastically improved the sampling and at the same time led to the identification of high energy barriers as cause for it. Consequently, simple strategies to overcome these barriers are to increase simulation time (computationally expensive) or to use enhanced sampling techniques such as Hamiltonian replica exchange molecular dynamics and one‐step perturbation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

On the relationship between the one‐electron and Bohm's quantum potential

The one‐electron potential, derived from the electron density, is a three‐dimensional function, whereas Bohm's quantum potential depends on the spatial coordinates of all involved electrons. To analyze the relationship between the two potentials in the many‐electron case, first the dimensionality of the quantum potential needs to be reduced to match that of the one‐electron potential. A possible approach for such dimensionality reduction by calculating the expectation value of the quantum potential over all but one electron, using the factorization of the real part of the wave function into a marginal and conditional function is presented, and a relation between such three‐dimensional local quantum potential and the one‐electron potential is given. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

SBA‐15 pore‐width decrease via a one‐ or a two‐step covalent bonding of a Fischer tungsten carbene as measured by N2 sorption

The chemical attachment of Fischer tungsten carbene molecules around the cylindrical walls of SBA‐15 causes a pore‐width diminution with respect to the diameters of the voids existing in the pristine substrate. The attachment is made via a bridging unit of aminopropyltriethoxysilane (APTES) that, at its ethoxysilane end, anchors on the SBA‐15 surface while, at its amino end, reacts with the tungsten carbene. The attachment can either be made in a single stage by adding the whole molecule, i.e. bridging + carbene units, or stepwise, i.e. the bridging unit is firstly attached to the silica surface and afterward the carbene group is linked to the amine end of the previous species. A remarkable result is that a uniform pore‐width decrease of 0.30 nm is achieved when the ethoxysilane bridging units are anchored on the SiO₂ surface; this decrease being independent of the pore size. An additional decrease of 0.37 nm is observed when the tungsten carbene is fixed to the amine end of the bridging molecule; the total pore‐width decrease is thus 0.67 nm. In turn, the one‐stage insertion of the whole carbene molecules causes a uniform pore‐width decrease of 0.78 nm. The central cores of the functionalized pore entities remain free for the molecular transport of species that are taking place in catalytic, separation, and controlled release processes. The chemical anchoring of molecules on the surface of SBA‐15 pores can be tailor sized and occlude the existing micropores, thus representing important and fundamental industrial applications. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of atomic pressure in the multiple time‐step integration algorithm

In molecular dynamics (MD) calculations, reduction in calculation time per MD loop is essential. A multiple time‐step (MTS) integration algorithm, the RESPA (Tuckerman and Berne, J. Chem. Phys. 1992, 97, 1990–2001), enables reductions in calculation time by decreasing the frequency of time‐consuming long‐range interaction calculations. However, the RESPA MTS algorithm involves uncertainties in evaluating the atomic interaction‐based pressure (i.e., atomic pressure) of systems with and without holonomic constraints. It is not clear which intermediate forces and constraint forces in the MTS integration procedure should be used to calculate the atomic pressure. In this article, we propose a series of equations to evaluate the atomic pressure in the RESPA MTS integration procedure on the basis of its equivalence to the Velocity‐Verlet integration procedure with a single time step (STS). The equations guarantee time‐reversibility even for the system with holonomic constrants. Furthermore, we generalize the equations to both (i) arbitrary number of inner time steps and (ii) arbitrary number of force components (RESPA levels). The atomic pressure calculated by our equations with the MTS integration shows excellent agreement with the reference value with the STS, whereas pressures calculated using the conventional ad hoc equations deviated from it. Our equations can be extended straightforwardly to the MTS integration algorithm for the isothermal NVT and isothermal–isobaric NPT ensembles. © 2017 Wiley Periodicals, Inc.     

CHARMM‐GUI ligand reader and modeler for CHARMM force field generation of small molecules

Reading ligand structures into any simulation program is often nontrivial and time consuming, especially when the force field parameters and/or structure files of the corresponding molecules are not available. To address this problem, we have developed Ligand Reader & Modeler in CHARMM‐GUI. Users can upload ligand structure information in various forms (using PDB ID, ligand ID, SMILES, MOL/MOL2/SDF file, or PDB/mmCIF file), and the uploaded structure is displayed on a sketchpad for verification and further modification. Based on the displayed structure, Ligand Reader & Modeler generates the ligand force field parameters and necessary structure files by searching for the ligand in the CHARMM force field library or using the CHARMM general force field (CGenFF). In addition, users can define chemical substitution sites and draw substituents in each site on the sketchpad to generate a set of combinatorial structure files and corresponding force field parameters for throughput or alchemical free energy simulations. Finally, the output from Ligand Reader & Modeler can be used in other CHARMM‐GUI modules to build a protein‐ligand simulation system for all supported simulation programs, such as CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, OpenMM, and CHARMM/OpenMM. Ligand Reader & Modeler is available as a functional module of CHARMM‐GUI at http://www.charmm-gui.org/input/ligandrm . © 2017 Wiley Periodicals, Inc.     

草酸锌空心纳米结构的一步固相合成及其表征

本文利用醋酸锌和草酸的一步低热固相化学反应制备了草酸锌空心纳米球，并通过在该反应体系中加入表面活性剂聚乙二醇400得到了草酸锌空心纳米链。采用X-射线粉末衍射（XRD）、透射电镜（TEM）、高倍透射电镜(HRTEM)、扫描电镜(SEM)、红外(IR) 以及热重-差热(TG/DTA)分析对所合成的样品进行了表征.     

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A multiple time step algorithm compatible with a large number of distance classes and an arbitrary distance dependence of the time step size for the fast evaluation of nonbonded interactions in molecular simulations

A new algorithm is introduced to perform the multiple time step integration of the equations of motion for a molecular system, based on the splitting of the nonbonded interactions into a series of distance classes. The interactions between particle pairs in successive classes are updated at a progressively decreasing frequency. Unlike previous multiple time-stepping schemes relying on distance classes, the present algorithm sorts interacting particle pairs by their next update times rather than by their update frequencies. For this reason, the proposed scheme is extremely flexible with respect to the number of classes that can be employed (up to hundred or more) and the distance dependence of the relative time step size (arbitrary integer function of the distance). It can also easily be adapted to classes defined based on a criterion other than the interparticle distance (e.g., interaction magnitude). Different variants of the algorithm are tested in terms of accuracy and efficiency for simulations of a pure water system (6167 molecules) under truncated-octahedral periodic boundary conditions, and compared to the twin-range method standardly used with GROMOS96 (short- and long-range cutoff distances of 0.8 and 1.4 nm, pair list and intermediate-range interactions updated every five steps). In particular, multiple time-stepping schemes with an accuracy comparable to that of the twin-range method can be designed, that permit to increase the effective (long-range) cutoff distance from 1.4 to 3.0 nm with a performance loss of only about a factor 2. This result is quite encouraging, considering the benefits of doubling the cutoff radius in the context of (bio-)molecular simulations.     

Efficiency of perturbation‐selection and its orbital dependence in the SAC‐CI calculations for valence excitations of medium‐size molecules

The efficiency and accuracy of the perturbation‐selection used in the symmetry‐adapted cluster‐configuration interaction (SAC‐CI) calculations are investigated for several low‐lying valence excited states of 21 medium‐size molecules, including typical chromophores with heterocyclic macrocycles (free‐base porphine, coumarin, indole, and BODIPY), nucleobases, amino acids (tyrosine and tryptophan), polycyclic aromatic hydrocarbons, and organometallics (ferrocene and Re(bpy) ). Benchmark SAC‐CI calculations with up to 110 million operators are performed. The efficiency of the perturbation‐selection depends on the molecular orbitals (MOs); therefore, the canonical MO and localized MO (LMO) obtained by Pipek‐Mezey's method are examined. Except for the highly symmetric molecules, using LMOs improves the efficiency and accuracy of the perturbation‐selection. With using LMOs and perturbation‐selection, sufficiently reliable results can be obtained in less than 10% of the computational costs required for the full‐dimensional calculations. The perturbation‐selection with LMOs is suggested to be a promising method for excited states in larger molecular systems. Copyright © 2014 Wiley Periodicals, Inc.     

Preparation of Keggin‐type phosphomolybdate by a one‐step solid‐state reaction at room temperature and its application in protein adsorption

Keggin‐type phosphomolybdate ((C₁₉H₄₂N)₃PMo₁₂O₄₀) is prepared by a one‐step solid‐state reaction at room temperature and characterized by scanning electron microscopy, Fourier transform infrared spectroscopy, X‐ray diffraction, thermogravimetric analysis, and elemental analysis. The as‐prepared phosphomolybdate is demonstrated to be an efficient adsorbent for proteins. In this particular case, the selective adsorption of neutral protein hemoglobin is achieved. While under the same conditions virtually no adsorption of acidic and basic proteins, represented by bovine serum albumin and cytochrome c, are observed. A solid‐phase extraction procedure is developed for the selective isolation of hemoglobin. At pH 6, a sorption efficiency of 91.4% is achieved for 100 μg/mL hemoglobin in 1.0 mL solution by using 5.0 mg of the phosphomolybdate. The adsorption behavior of hemoglobin fits well with a Langmuir adsorption model, corresponding to a theoretical adsorption capacity of 55.86 mg/g. The retained hemoglobin could be readily recovered by using a 60 mmol/L imidazole solution at pH 7, giving rise to a recovery of 64.7%. The practical application of phosphomolybdate for protein adsorption is demonstrated by the selective isolation of hemoglobin from human whole blood followed by a sodium dodecyl sulfate polyacrylamide gel electrophoresis assay.     

One‐step synthesis of block copolymers using a hydroxyl‐functionalized trithiocarbonate RAFT agent as a dual initiator for RAFT polymerization and ROP

A range of well‐defined block copolymers were synthesized using 4‐cyano‐4‐(dodecylsulfanylthiocarbonyl)sulfanylpentanol (CDP) as a dual initiator for reversible addition‐fragmentation chain transfer (RAFT) polymerization and ring‐opening polymerization (ROP) in a one‐step process. Styrene, (meth)acrylate, and acrylamide monomers were polymerized in a controlled manner for one block composed of vinyl monomers, and δ‐valerolactone (VL), ε‐caprolactone (CL), trimethylene carbonate (TMC), and L ‐lactide (LA) were used for the other block composed of cyclic monomers. Diphenyl phosphate was used as a catalyst for the ROP of VL, CL, and TMC, and 4‐dimethyamino pyridine for the ROP of LA. These catalysts did not interfere with RAFT polymerization and the synthesis of various block copolymers proceeded in a controlled manner. CDP was found to be a very useful dual initiator for a one‐step synthesis of various block copolymers by a combination of RAFT polymerization and ROP. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013