The temperature intervals with global exchange of replicas empirical accelerated sampling method: parameter sensitivity and extension to a complex molecular system

The recently developed "temperature intervals with global exchange of replicas" (TIGER2) algorithm is an efficient replica-exchange sampling algorithm that provides the freedom to specify the number of replicas and temperature levels independently of the size of the system and temperature range to be spanned, thus making it particularly well suited for sampling molecular systems that are considered to be too large to be sampled using conventional replica exchange methods. Although the TIGER2 method is empirical in nature, when appropriately applied it is able to provide sampling that satisfies the balance condition and closely approximates a Boltzmann-weighted ensemble of states. In this work, we evaluated the influence of factors such as temperature range, temperature spacing, replica number, and sampling cycle design on the accuracy of a TIGER2 simulation based on molecular dynamics simulations of alanine dipeptide in implicit solvent. The influence of these factors is further examined by calculating the properties of a complex system composed of the B1 immunoglobulin-binding domain of streptococcal protein G (protein G) in aqueous solution. The accuracy of a TIGER2 simulation is particularly sensitive to the maximum temperature level selected for the simulation. A method to determine the appropriate maximum temperature level to be used in a TIGER2 simulation is presented.     

Gradient SHAKE: An improved method for constrained energy minimization in macromolecular simulations

Current macromolecular energy minimization algorithms become inefficient and prone to failure when bond length constraints are imposed. They are required to relieve steric stresses in biomolecules prior to a molecular dynamics simulation. Unfortunately, the latter often require constraints, leading to difficulties in initiating trajectories from unconstrained energy minima. This difficulty was overcome by requiring that the components of the energy gradient vanish along the constrained bonds. The modified energy minimization algorithm converges to a lower energy in a fewer number of iterations and is more robust than current implementations. The method has been successfully applied to the Dickerson DNA dodecamer, CGCGAATTCGCG. © 1995 John Wiley & Sons, Inc.     

Characterization of conformational equilibria through Hamiltonian and temperature replica-exchange simulations: assessing entropic and environmental effects

Molecular dynamics simulations based on the replica-exchange framework (REMD) are emerging as a useful tool to characterize the conformational variability that is intrinsic to most chemical and biological systems. In this work, it is shown that a simple extension of the replica-exchange method, known as Hamiltonian REMD, greatly facilitates the characterization of conformational equilibria across large energetic barriers, or in the presence of substantial entropic effects, overcoming some of the difficulties of REMD based on temperature alone. In particular, a comparative assessment of the HREMD and TREMD approaches was made, through computation of the gas-phase free-energy difference between the so-called D(2d) and S(4) states of tetrabutylammonium (TBA), an ionic compound of frequently used in biophysical studies of ion channels. Taking advantage of the greater efficiency of the HREMD scheme, the conformational equilibrium of TBA was characterized in a variety of conditions. Simulation of the gas-phase equilibrium in the 100-300 K range allowed us to compute the entropy difference between these states as well as to describe its temperature dependence. Through HREMD simulations of TBA in a water droplet, the effect of solvation on the conformational equilibrium was determined. Finally, the equilibrium of TBA in the context of a simplified model of the binding cavity of the KcsA potassium channel was simulated, and density maps for D(2d) and S(4) states analogous to those derived from X-ray crystallography were constructed. Overall, this work illustrates the potential of the HREMD approach in the context of computational drug design, ligand-receptor structural prediction and more generally, molecular recognition, where one of the most challenging issues remains to account for conformational flexibility as well for the solvation and entropic effects thereon.     

Stiffness and energy conservation in molecular dynamics: An improved integrator

Molecular dynamics is the integration of a set of coupled differential equations describing the motion of atoms over time. These equations exhibit the unfortunate property of stiffness, that is, terms of the equations (the forces on the atoms) are defined on several scales—ranging from tens of kcal/mol/Å to thousands of kcal/mol/Å. Additional nonconservative and stiff effects occur when a distance cutoff is used for the electrostatics and nonbonded potentials. Because the first derivative at the cutoff is essentially infinite, small variations in positions will cause large variations in energy and violate conservation of energy. The effects are demonstrated in a small system of 125 isolated water molecules. It is possible to greatly reduce and nearly eliminate the stiff integration effects with an improved integrator. The nonconservative effects of the distance cutoff cannot be removed by changing the integrator. © John Wiley & Sons, Inc.     

An improved SCPF scheme for polarization energy calculations

Convergence of the Self-Consistent Polarization Field (SCPF) method of polarization energy calculations for organic molecular materials is analysed. Use of the Conjugate Gradients method for solving the SCPF equations is proposed. Efficiency of both the original and the newly proposed approach is compared for selected model systems. Brief discussion of the factors influencing the performance of Krylov-space-based methods for polarization energy calculations is presented.     

An improved LCAO-MO-SCF π-electron method

Using the method of a previous paper a modified technique is used to calculate the core parameters for carbon, nitrogen and oxygen atoms. The one-center core parameters H _pp ⁰ , are identified with conventional atomic valence state ionization potentials. The two-center core parameters are given by the equation H _pq ⁰ = (H _pp ⁰ + H _qq ⁰ )/2 (H _pq – 0.0855 R _pq + 0.24639) – n _p (S _pq /4)( _pp + _pq ) – n _q (S _pq /4) · ( _qq + _pq ).It is shown that these parameters, along with the electron repulsion integrals adopted earlier allow one to calculate with reasonable accuracy the singlet spectra and ionization potentials (within Koopmans' approximation) of a large number of unsaturated hydrocarbons as well as the heterocycles pyridine, p-benzoquinone (PBQ), pyrrole and furan.

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Zusammenfassung Unter Benutzung einer früheren Methode wird ein modifiziertes Verfahren zur Berechnung der Rumpfparameter von C-, N- und O-Atomen vorgeschlagen. Die Einzentren-Rumpfparameter H _pp ⁰ werden den üblichen Ionisationspotentialen für die atomaren Valenzzustände gleichgesetzt. Die Zweizentren-Rumpfparameter werden nach H _pq ⁰ = (H _pp ⁰ + H _qq ⁰ )/2 (H _pq – 0.0855 R _pq + 0.24639) – n _p (S _pq /4)( _pp + _pq ) – n _q (S _pq /4) · ( _qq + _pq ) berechnet.Auf diese Weise und unter Verwendung der schon früher benützten Coulombintegrale lassen sich die Singulett-Spektren und Ionisationspotentiale einer großen Anzahl ungesättigter Kohlenwasserstoffe sowie der Heterocyclen Pyridin, p-Benzochinon, Pyrrol und Furan mit der üblichen Genauigkeit berechnen.

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Résumé Calcul des paramètres de coeur du carbone, de l'azote et de l'oxygène, en utilisant la méthode d'un article précédent techniquement modifiée. Les paramètres de coeur monocentriques H _pp ⁰ sont identifiés avec les potentiels d'ionisation de l'état atomique de valence conventionnel. Les paramètres de coeur bicentriques sont donnée par l'équation H _pq ⁰ = (H _pp ⁰ + H _qq ⁰ )/2 (H _pq – 0.0855 R _pq + 0.24639) – n _p (S _pq /4)( _pp + _pq ) – n _q (S _pq /4) · ( _qq + _pq ). On montre que ces paramètres utilisés avec les intégrales de répulsion précédemment adoptées permettent de calculer avec une précision raisonnable le spectresingulet et les potentiels d'ionisation (dans l'approxirnation de Koopmans) pour un grand nombre d'hydrocarbures non saturés et des hétérocycles commee la pyridine, la p-benzoquinone (PBQ), le pyrrole et le furane.

     

5,7-二甲氧基香豆素合成方法的改进

以间苯三酚为原料,选甲醇进行甲基化反应制备3,5-二甲氧基苯酚,以丙炔酸乙酯经Pechmann环化反应制备了白柠檬素(5,7-二甲氧基香豆素)。考察了甲基化反应、环化反应的影响因素,结果表明n(间苯三酚)∶n(甲醇)=1∶15,干燥氯化氢为催化剂,75℃反应7h,甲基化收率为82%;n(丙炔酸乙酯)∶n(3,5-二甲氧基苯酚)∶n(无水氯化锌)=1∶3∶1,环化温度为100℃,N2保护下反应2h,环化反应收率为88%,两步反应总收率达73%。目标产物用红外、质谱、核磁分析手段进行了表征和分析。     

Q-fit: a probabilistic method for docking molecular fragments by sampling low energy conformational space

A new method is presented that docks molecular fragments to a rigid protein receptor. It uses a probabilistic procedure based on statistical thermodynamic principles to place ligand atom triplets at the lowest energy sites. The probabilistic method ranks receptor binding modes so that the lowest energy ones are sampled first. This allows constraints to be introduced to limit the depth of the search leading to a computationally efficient method of sampling low energy conformational space. This is combined with energy minimization of the initial fragment placement to arrive at a low energy conformation for the molecular fragment. Two different search methods are tested involving (i) geometric hashing and (ii) pose clustering methods. Ten molecular fragments were docked that have commonly been used to test docking methods. The success rate was 8/10 and 10/10 for generating a close solution ranked first using the two different sampling procedures. In general, all five of the top ranked solutions reproduce the observed binding mode, which increases confidence in the predictions. A set of ten molecular fragments that have previously been identified as problematic were docked. Success was achieved in 3/10 and 4/10 using the two different methods. Again there is a high level of agreement between the two methods and again in the successful cases the top ranked solutions are correct whilst in the case of the failures none are. The geometric hashing and pose clustering methods are fast averaging 13 and 11 s per placement respectively using conservative parameters. The results are very encouraging and will facilitate the process of finding novel small molecule lead compounds by virtual screening of chemical databases.     

Enveloping distribution sampling: a method to calculate free energy differences from a single simulation

The authors present a method to calculate free energy differences between two states A and B "on the fly" from a single molecular dynamics simulation of a reference state R. No computer time has to be spent on the simulation of intermediate states. Only one state is sampled, i.e., the reference state R which is designed such that the subset of phase space important to it is the union of the parts of phase space important to A and B. Therefore, an accurate estimate of the relative free energy can be obtained by construction. The authors applied the method to four test systems (dipole inversion, van der Waals interaction perturbation, charge inversion, and water to methanol conversion) and compared the results to thermodynamic integration estimates. In two cases, the enveloping distribution sampling calculation was straightforward. However, in the charge inversion and the water to methanol conversion, Hamiltonian replica-exchange molecular dynamics of the reference state was necessary to observe transitions in the reference state simulation between the parts of phase space important to A and B, respectively. This can be explained by the total absence of phase space overlap of A and B in these two cases.     

Efficient global biopolymer sampling with end-transfer configurational bias Monte Carlo

We develop an "end-transfer configurational bias Monte Carlo" method for efficient thermodynamic sampling of complex biopolymers and assess its performance on a mesoscale model of chromatin (oligonucleosome) at different salt conditions compared to other Monte Carlo moves. Our method extends traditional configurational bias by deleting a repeating motif (monomer) from one end of the biopolymer and regrowing it at the opposite end using the standard Rosenbluth scheme. The method's sampling efficiency compared to local moves, pivot rotations, and standard configurational bias is assessed by parameters relating to translational, rotational, and internal degrees of freedom of the oligonucleosome. Our results show that the end-transfer method is superior in sampling every degree of freedom of the oligonucleosomes over other methods at high salt concentrations (weak electrostatics) but worse than the pivot rotations in terms of sampling internal and rotational sampling at low-to-moderate salt concentrations (strong electrostatics). Under all conditions investigated, however, the end-transfer method is several orders of magnitude more efficient than the standard configurational bias approach. This is because the characteristic sampling time of the innermost oligonucleosome motif scales quadratically with the length of the oligonucleosomes for the end-transfer method while it scales exponentially for the traditional configurational-bias method. Thus, the method we propose can significantly improve performance for global biomolecular applications, especially in condensed systems with weak nonbonded interactions and may be combined with local enhancements to improve local sampling.     

A convective replica‐exchange method for sampling new energy basins

Replica‐exchange is a powerful simulation method for sampling the basins of a rugged energy landscape. The replica‐exchange method's sampling is efficient because it allows replicas to perform round trips in temperature space, thereby visiting both low and high temperatures in the same simulation. However, replicas have a diffusive walk in temperature space, and the round trip rate decreases significantly with the system size. These drawbacks make convergence of the simulation even more difficult than it already is when bigger systems are tackled. Here, we present a simple modification of the exchange method. In this method, one of the replicas steadily raises or lowers its temperature. We tested the convective replica‐exchange method on three systems of varying complexity: the alanine dipeptide in implicit solvent, the GB1 β‐hairpin in explicit solvent and the Aβ_25–35 homotrimer in a coarse grained representation. For the highly frustrated Aβ_25–35 homotrimer, the proposed “convective” replica‐exchange method is twice as fast as the standard method. It discovered 24 out of 27 free‐energy basins in less than 500 ns. It also prevented the formation of groups of replicas that usually form on either side of an exchange bottleneck, leading to a more efficient sampling of new energy basins than in the standard method. © 2012 Wiley Periodicals, Inc.     

An improved actinide separation method for environmental samples

This paper presents a rapid method of separation of five actinide elements (Th, U, Np, Pu, and Am) for aqueous media samples. This separation method utilizes the unique chemistries of the actinides at low concentrations^1,2 and the properties of the EIChroM TRU-Resin^TM extraction resin. In order to cleanly recover the five actinides from aqueous samples or solubilized soil samples, the sample is passed through the column twice. The sample is first loaded in an HCl solution with hydrogen peroxide. This allows the Am and most matrix ions to pass through the column. Then the Th is eluted using dilute HCl followed by the Np and Pu which are eluted together with oxalic acid in dilute HCl solution. Finally, the U is eluted with ammonium oxalate solution. A calcium-oxalate coprecipitation is performed on the original load solution containing the Am ions and the dissolved precipitate is then reloaded onto the TRU-Resin^TM column in HNO₃ with ascorbic acid. The procedure requires approximately 1.5 working days for experienced technicians, greatly reduces waste, and generally results in actinide recoveries of 80–100%.     

An improved residue analytical method for phenylurea herbicides

Summary An improved HPLC method with electrochemical detection is applied to the determination of phenyl urea herbicide residues in crops. The analysis includes extraction and hydrolysis with NaOH, clean-up by steam distillation and partition into methanol/HCl and quantitation of the aniline by HPLC with 2-column switching technique and amperometric detection.     

Adaptive lambda square dynamics simulation: An efficient conformational sampling method for biomolecules

A novel, efficient sampling method for biomolecules is proposed. The partial multicanonical molecular dynamics (McMD) was recently developed as a method that improved generalized ensemble (GE) methods to focus sampling only on a part of a system (GEPS); however, it was not tested well. We found that partial McMD did not work well for polylysine decapeptide and gave significantly worse sampling efficiency than a conventional GE. Herein, we elucidate the fundamental reason for this and propose a novel GEPS, adaptive lambda square dynamics (ALSD), which can resolve the problem faced when using partial McMD. We demonstrate that ALSD greatly increases the sampling efficiency over a conventional GE. We believe that ALSD is an effective method and is applicable to the conformational sampling of larger and more complicated biomolecule systems. © 2013 Wiley Periodicals, Inc.     

二溴卡宾产生方法的改进

研究了用超声和相转催化结合使溴仿与固体氢氧化钠反应生成二溴卡宾的改良方法. 用这一方法只需20-30分钟就可以在烯烃存在下获得高得率的1,1-二溴环丙烷, 并且具有更方便的纯化过程.     

An improved solution-tight electrode holder for variable temperature electrochemical studies

With the help of oscillopolarographic methods, the formation of additional adsorption-desorption peaks or incisions in the curves i=f(E) and dE/dt=f(E) was observed for saturated solutions of higher fatty acids in 1 M H₂SO₄. In virtue of the analysis of the first and second polarization cycle, it was found, that, a previous electrode polarization to the adsorption potentials was necessary, if the additional peaks were to be formed. A supposition was made, that the additional peaks originate in the desorption and adsorption of the dimerized molecules of the acids.     

An improved method of constructive enumeration of graphs

A canonical numbering of molecular graphs based on the maximum code assigned to the lower-triangle part of the adjacency matrix is used for a recurrent constructive enumeration of molecular graphs. The underlying theoretical concept - the so-called semicanonical numbering - is much more restrictive than the originally used concept of cooperative numbering. The method does not involve very time-consuming isomorphism checks of currently constructed graphs against those already constructed.