Free energy calculation of single molecular interaction using Jarzynski's identity method:the case of HIV-1 protease inhibitor system

Jarzynski＇ identity （JI） method was suggested a promising tool for reconstructing free energy landscape of biomolecular interactions in numerical simulations and ex- periments. However, JI method has not yet been well tested in complex systems such as ligand-receptor molecular pairs. In this paper, we applied a huge number of steered molec- ular dynamics （SMD） simulations to dissociate the protease of human immunodeficiency type I virus （HIV-1 protease） and its inhibitors. We showed that because of intrinsic com- plexity of the ligand-receptor system, the energy barrier pre- dicted by JI method at high pulling rates is much higher than experimental results. However, with a slower pulling rate and fewer switch times of simulations, the predictions of JI method can approach to the experiments. These results sug- gested that the JI method is more appropriate for reconstruct- ing free energy landscape using the data taken from experi- ments, since the pulling rates used in experiments are often much slower than those in SMD simulations. Furthermore, we showed that a higher loading stiffness can produce higher precision of calculation of energy landscape because it yields a lower mean value and narrower bandwidth of work distri- bution in SMD simulations.

Analysis of a Critical Residue Determining Herbicide Efficiency Sensitivity in Carboxyltransferase Domain of Acetyl-CoA Carboxylase from Poaceae by Homology Modeling and Free Energy Simulation

Carboxyltransferase domain（CT） of acetyl-coenzyme A carboxylase（ACCase, EC 6.4.1.2） from a family of Poaceae is an important target of commercial herbicide APPs for controlling grass weed growth. As the abuse of APPs herbicides, the resistant ACCase due to the mutation of a single residue（Ile→Leu）, which is located in CT active site, is emergent in many populations and species of Poaceae. So it is urgent to understand the resistant mechanism so as to design new effect herbicides. Herein lies the complex of CT dimmer from Lolium rigidum and herbicide haloxyfop successfully constructed for wild type enzyme and Ile/Leu mutant, respectively, providing a basis for explaining the resistance from microscopic structure. Moreover, the binding free energy difference between wild type and mutant enzymes was predicted in good agreement with the known observation, and the various contributions to it were analyzed, by Molecular mechanics-Poisson-Boltzmann surface area（MM-PBSA） method. The results indicate the van der Waals interaction difference between the protein and inhibitor, -22.94 kJ/mol of CT wild type lower than that of mutant, is the major reason for resistance. Structure analysis further suggests that van der Waals interaction difference is originated from the steric hindrance between the side chain of mutated residue Leu and the chiral methyl group of haloxyfop. All these findings enhance the understanding of resistant mechanism of ACCase to herbicide by Ile/Leu mutation and provide an important clue for the rational design of high effective herbicides.

A SIMPLE METHOD TO CALCULATE RESONANCE ENERGY

A very simple method to calculate resonance energies of conjugated hydrocarbons by counting carbon numbers was introduced.

A NEW AB INITIO CALCULATION METHOD OF INNER-SPHERE REORGANIZATION ENERGY

On the basis of the-improved self-exchange model of reorganization phenomenon and accurate potential functions from ab initio calculation at HFSCF 6-31G* and DZP levels a new calculation method was,presented for the inner-sphere reorganization energy, values for diatomic molecular redox couples in gas phase electron transfer process have been calculated. Results agree well with the experimental data, and the effectiveness and importance of this method have been demonstrated for calculation of inner-sphere reorganization energy in gas phase electron transfer process.

Calculation of the Surface Energy of Pure Titanium

Anodic oxidation on pure titanium(α-Ti) surface causes the formation ofinterferential films with different colours,mainly golden,pink and blue.The col-our changes with the thickness of the ox-ide film.One of the factors,which influ-ences the growth rate of the film,may bethe grain surface energy.at least at the

Calculation of Neutral Particle Energy Spectra in Tokamak by Using the Monte Carlo Method

Neutral particle energy spectra in the HT-7 tokamak are calculated by using the Monte Carlo method. It can reproduce the spectra measured in experiment. Differences of neutral particle energy spectra in higher and lower electron density plasma are discussed. Results show that the ion temperature given by neutral particle energy spectra is lower than the real ion temperature, but the deviation is within 10% if the ion temperature is less than 800 eV and thecentral chord-averaged electron density does not exceed 3 ×1013 cm-3. But for ion temperature higher than 1000 eV at the central chord-averaged density limit up to 5 ×1013 cm-3, the neutral particle energy spectra can still give the ion temperature within 10% deviation.

Relativistic Reduction of the Electron-Nucleus Force in Bohr’s Hydrogen Atom and the Time of Electron Transition between the Neighbouring Quantum Energy Levels

The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.

Inclusion Modes of Berberine with β-Cyclodextrin in Aqueous Solution

The possible inclusion modes of berberine（Berb） with β-cyclodextrin（BCD） in aqueous solution were predicted by molecular docking,molecular dynamics（MD） simulation and binding free energy calculations.Firstly,the molecular docking result reveals that the docking conformations of Berb appeared in two clusters ranked in two opposite orientations.Then,10 ns MD simulation was performed separately on the lowest energy conformation of each orientation（Mode I and Mode II） obtained by molecular docking.Moreover,based on the trajectories from MD simulation,the binding free energies of the two different modes were calculated by the Molecular Mechanics/Poisson Boltzmann surface area（MM/PBSA） method.Through analyzing the binding free energies of Berb with BCD,we found that Mode II was the preferential inclusion mode,which was in good agreement with the experimental result.In addition,the computed results show that the main impetus for the complex was the van der Waals interaction,but the solvation energy and the entropy change produced an adverse effect on the complex.

Rapidly calculating the partition function of macroscopic systems

It has remained an open problem to accurately compute the partition function of macroscopic systems since the establishment of statistical physics. A rapid method approaching this problem was presented and was strictly tested by molecular dynamic （MD） simulations on Ar atoms in both dense gaseous and liquid states. The outcomes from the method on the internal energy and the work of isothermal expansion （and therefore the free energy） are in good agreement with the MD simulations, suggesting the method would be immediately applied in vast areas.

Hydrothermal Synthesis and Crystal Structure of a Microporous Gallophosphate with 12-Membered Ring Channels:Ga_9(PO_4)_(12)(H_3TREN)(H_2TREN)_3·xH_2O

An open-framework gallophosphate, Ga_9(PO_4)_ 12[(H_3TREN)(H_2TREN)_3]·xH_2O was hydrothermally synthesized at 453 K with tris(2-aminoethyl) amine(TREN) as the organic template and characterized by single-crystal X-ray diffraction. Ga_9(PO_4)_ 12[(H_3TREN)(H_2TREN)_3]·xH_2O crystallized in a cubic space group I43m, with a=1.68552(3) nm and Z=2. The structure contains 12-membered ring channels and supercages of 1.434 nm in diameter, and is an analogue of Al_9(PO_4)_ 12(C_ 24H_ 91N_ 16)·17H_2O. Template-TREN in the supercage was different from triethylenetetraamine(TETA) used in the initial reaction mixture due to the construction transformation. The TETAs transformed into the TRENs due to the low interaction energy between the template and framework. We verified it via energy calculation and liquid state NMR.

Influence of Isotope Effects on Product Polarizations of N(~2D)+D_2, N(~2D)+H_2 and N(~2D)+HD Reactive Systems

To figure out the influence of isotope effect on product polarizations of the N（2D）＋D2 reactive system and its isotope variants, quasi-classical trajectory（QCT） calculation was performed on Ho＇s potential energy surface（PES） of 2A″ state. Product polarizations such as product distributions of P（θr）, P（φr） and P（θr,φr）, as well as the generalized polarization-dependent differential cross sections（PDDCSs） were discussed and compared in detail among the four product channels of the title reactions. Both the intermolecular and intramolecular isotope effects were proved to be influential on product polarizations.

Think Home: A Smart Home as Digital Ecosystem

This work brings all new and advanced technology which is proposed for refinement and improvement in the existing electrification system at domestic as well as commercial levels including hotels, commercial complexes, apartments, rented floors and rooms. This advanced module will not only convey means of luxury but will also accomplish real-time energy monitoring and cost es-timation. This developed module will rule out entire re-wiring and will be fruitful at places where installation of a new meter was a problem. The new system after installation will offer means of comfort to the consumer, elderly as well as handicapped and disabled people in operating electric load with ease and comfort. Apart from this, it would also benefit the apartment/hotel owner’s and business personnel who have rented their property or portion of property and face problems in calculating energy bill.

Planck’s Oscillators at Low Temperatures and Haken’s Perturbation Approach to the Quantum Oscillators Reconsidered

In the first step the extremal values of the vibrational specific heat and entropy represented by the Planck oscillators at the low temperatures could be calculated. The positions of the extrema are defined by the dimensionless ratios between the quanta of the vibrational energy and products of the actual temperature multiplied by the Boltzmann constant. It became evident that position of a local maximum obtained for the Planck’s average energy of a vibration mode and position of a local maximum of entropy are the same. In the next step the Haken’s time-dependent perturbation approach to the pair of quantum non-degenerate Schr?dinger eigenstates of energy is re-examined. An averaging process done on the time variable leads to a very simple formula for the coefficients entering the perturbation terms.

Classification and Location Scheme Selection of Coupling Components in Integrated Electrical and Heating Systems with Renewable Energy

Integrated energy systems(IES)are under development to accommodate the widespread penetration of renewable energy into power systems.The universal utilization of coupling components makes the connection between power grids and heat grids even closer.This paper applies energy flow calculations to planning problems and explores a method for selecting coupling components in the integrated electrical and heating systems.This process is based on the analysis of energy flow distribution and the comprehensive indexes,which include operation cost and the penalty cost of wind curtailment and solar energy curtailment.Besides,a selection method of coupling components installation locations based on energy flow calculations is provided.At last,an IES with 5 electrical buses and 5 heating nodes,and a 9-bus electrical power system with a 31-node heating transmission system are chosen to study the specific application problems in detail as well as to elucidate the effectiveness of the proposed method.It turned out that the relevant coupling components and their positions can be selected according to the indexes obtained by integrated electrical-hydraulic-thermal calculation.This proposed method is conducive to the planning of integrated energy systems.

Output formation tracking for networked systems with limited energy and aperiodic silence

For leader-following networked systems with the topology switching and the aperiodic silence,limited-energy output formation tracking problems are investigated.Firstly,a new output formation tracking control protocol is proposed,which contains two components associated with the communication interactions between the leader and tracking intelligent agents and the communication interactions among tracking intelligent agents,respectively,and the aperiodic silence,the topology switching and the energy constraint index is introduced properly.Then,a two-step transformation method is presented to separate the whole dynamics of a networked system into the relative dynamics between the leader and tracking intelligent agents and the dynamics of the leader,and sufficient conditions for limited-energy output formation tracking for networked systems with limited energy and aperiodic silence are presented,which are extended into networked systems without the aperiodic silence.Especially,a partition checking algorithm is presented to check limitedenergy output formation tracking design criteria.Finally,a numerical example is illustrated to demonstrate the validness of theoretical results.

Ab initio calculations on accurate dissociation energy, equilibrium geometry, and analytic potential energy function for the 6~3Π state of ~7LiH molecule

The accurate dissociation energy and equilibrium geometry of the ball state of ^7LiH molecule is calculated using a symmetry-adapted-cluster configuration-interaction method in full active space. And the calculated results are 0.2580 eV and 0.1958 nm for the dissociation energy and equilibrium geometry, respectively. The whole potential energy curve for the b^3∏ state is also calculated over the internuclear separation range from about 0.10 to 0.54 nm. The results are fitted by the Murrell-Sorbie function. It is found that the Murrell-Sorbie function form, which is mainly used to fit the ground-state potential energy function, is well suitable for the excited triplet b^3∏ state. The vertical excitation energy from the ground state to the b^3∏ state is calculated to be 4.233 eV. Based on the analytic potential energy function, the harmonic frequency of 610.88 cm^-1 about this state is firstly estimated. Compared with other theoretical results, this work is the most complete effort to deal with the analytic potential energy function and the harmonic frequency of this state.

Calculation of vibrational energy transition rates in acoustic relaxation processes for excitable gas molecules

To research the correlation between vibrational energy transition rates and acoustic relaxation processes in excitable gases, the vibrational relaxation theory provided by Tanczos [J. Chem. Phy3. 25, 439 （1956）] is applied to calculate the energy transition rates of Vibrational- Vibrational （V-V） and Vibrational-Translational （V-T） energy transfer in gas mixtures. The results of calculation for the multi-relaxation processes in various gas mixtures, consisting of carbon dioxide, methane, chlorine, nitrogen, and oxygen at room temperature, demonstrate that the acoustic energy stagnated in every vibrational mode is coupled with each other through V-V energy exchanges. The vibrational excitation energy will relax through the V-T de-excitation path of the lowest mode because of its fastest V-T transition rate, resulting in that only one absorption peak can be measured for most of excitable gas mixtures. Thus, an effective model is provided to analyze how the vibrational energy transition rates affect the characteristics of acoustic relaxation processes and acoustic propagation in excitable gas mixtures.

CALCULATION OF THE HYDRODYNAMIC CHARACTERISTICS OF A OWC WAVE ENERGY ABSORBER

This paper deals with the hydrodynamic response to waves of a 3-D OWC(oscillating water column)wave energy absorber with converging channel.The theoretical solutions are presented by means of three-dimensional GREEN function method.In the calculation,the flow field is divided into two subregions:an inside field and an outside one.In the outside field the solution is represented by oscillating sources distributed on the outer surface of the chamber of the absorber,while the solution of the inside field is expressed by Rakine source-distribution on the inner surface of the chamber.Both solutions are matched on the artificial interface.The calculated.values seem to agree reasonably well with experimental results.

Investigation on the potential barrier to internal rotation in molecules——Ab initio calculation and energy partition of the internal rotation barrier in complex molecule H_3N-BH_3

Based on the ab initio/6-31Gcalculation, the potential barrier to internal rotation in mol-ecule HN--BHhas been studed by means of PD/LSF atomic charge model and Buckingham（exp--6-1）energy partition method. The results indicate that the order of the contributions of the componentsto the total energy barrier △E is |△V|（electrostatic） >|△V| （charge transfer）>|△V| （exchangerepulsion）>|△V| （dispersion）. For △Vthere are maxima at θ= 30°and 90°, and a saddle atθ= 60°. There are good linear relationships for the total barrier △E, △Vand △Vwith cos3θrespectively, and the same for the dipole moment from PD/LSF model (μ) and that from abinitio calculation (μ) vs. cos3θ respectively.

Discovery of new characterizations of parameter distributions in a semiempirical mass model:an investigation by dividing an overdetermined system into numerous balanced subsystems

We propose and test a new method of estimating the model parameters of the phenomenological BetheWeizsacker mass formula.Based on the Monte Carlo sampling of a large dataset,we obtain,for the first time,a Cauchy-type parameter distribution formed by the exact solutions of linear equation systems.Using the maximum likelihood estimation,the location and scale parameters are evaluated.The estimated results are compared with those obtained by solving overdetermined systems,e.g.,the solutions of the traditional least-squares method.Parameter correlations and uncertainty propagation are briefly discussed.As expected,it is also found that improvements in theoretical modeling(e.g.,considering microscopic corrections)decrease the parameter and propagation uncertainties.