scholarly journals Energy Minimization

2020 ◽  
Author(s):  
Budhayash Gautam
Keyword(s):  
Energy Minimization ◽  
Minimum Energy ◽  
Electrostatic Energy ◽  
Covalent Bonds ◽  
Energy Accounting ◽  
Energetic State ◽  
Indispensable Tool ◽  
The Given ◽  
Short Contacts ◽  
Atomic Coordinates

The energetic state of a protein is one of the most important representative parameters of its stability. The energy of a protein can be defined as a function of its atomic coordinates. This energy function consists of several components: 1. Bond energy and angle energy, representative of the covalent bonds, bond angles. 2. Dihedral energy, due to the dihedral angles. 3. A van der Waals term (also called Leonard-Jones potential) to ensure that atoms do not have steric clashes. 4. Electrostatic energy accounting for the Coulomb’s Law m protein structure, i.e. the long-range forces between charged and partially charged atoms. All these quantitative terms have been parameterized and are collectively referred to as the ‘force-field’, for e.g. CHARMM, AMBER, AMBERJOPLS and GROMOS. The goal of energy Minimization is to find a set of coordinates representing the minimum energy conformation for the given structure. Various algorithms have been formulated by varying the use of derivatives. Three common algorithms used for this optimization are steepest descent, conjugate gradient and Newton–Raphson. Although energy Minimization is a tool to achieve the nearest local minima, it is also an indispensable tool in correcting structural anomalies, viz. bad stereo-chemistry and short contacts. An efficient optimization protocol could be devised from these methods in conjunction with a larger space exploration algorithm, e.g. molecular dynamics.

scholarly journals Validation of molecular crystal structures from powder diffraction data with dispersion-corrected density functional theory (DFT-D)

2014 ◽  
Vol 70 (6) ◽  
pp. 1020-1032 ◽  
Author(s):  
Jacco van de Streek ◽  
Marcus A. Neumann
Keyword(s):  
Density Functional Theory ◽  
Crystal Structures ◽  
Powder Diffraction ◽  
Energy Minimization ◽  
Molecular Crystal ◽  
Density Functional ◽  
Powder Diffraction Data ◽  
High Quality ◽  
Functional Theory ◽  
Atomic Coordinates

In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published in an IUCr journal were energy-minimized with DFT-D and compared to the SX benchmark. The on average slightly less accurate atomic coordinates of XRPD structures do lead to systematically higher root mean square Cartesian displacement (RMSCD) values upon energy minimization than for SX structures, but the RMSCD value is still a good indicator for the detection of structures that deserve a closer look. The upper RMSCD limit for a correct structure must be increased from 0.25 Å for SX structures to 0.35 Å for XRPD structures; the grey area must be extended from 0.30 to 0.40 Å. Based on the energy minimizations, three structures are re-refined to give more precise atomic coordinates. For six structures our calculations provide the missing positions for the H atoms, for five structures they provide corrected positions for some H atoms. Seven crystal structures showed a minor error for a non-H atom. For five structures the energy minimizations suggest a higher space-group symmetry. For the 225 SX structures, the only deviations observed upon energy minimization were three minor H-atom related issues. Preferred orientation is the most important cause of problems. A preferred-orientation correction is the only correction where the experimental data are modified to fit the model. We conclude that molecular crystal structures determined from powder diffraction data that are published in IUCr journals are of high quality, with less than 4% containing an error in a non-H atom.

scholarly journals An Absolute-value Detector with Threshold Comparing for Spike Detection in Brain-machine Interface

2021 ◽  
Vol 2113 (1) ◽  
pp. 012038
Author(s):  
Mingzheng Yuan
Keyword(s):  
Energy Consumption ◽  
Input Data ◽  
Minimum Energy ◽  
Full Adder ◽  
Brain Machine Interface ◽  
Optimized Design ◽  
Spike Detection ◽  
Absolute Value ◽  
Machine Interface ◽  
The Given

Abstract This research designs an absolute-value detector with the function of threshold comparing. Specifically, it is an essential device in the spike detection of the brain-machine interface. The optimized design in the research can accomplish the main functions in spike detection and has good performance in both delay and energy consumption. It comes up with two types of design at the beginning. To make the design reliable and comprehensive, it decides to discuss both methods in this paper. The first design is using a full adder, multiplexer and comparator. The concept of its logic circuit is adding the logic one to the input when the given input data is negative, keeping the original information as the given input data is positive. To achieve the function of adding, this study chooses the full adders. The primary purpose of using multiplexers is to select from the processed input and original input, and the choice depends on the most significant bit (MSB) of the input data. To compare the absolute value of the input data with a given threshold, this research used a multi-bit comparator. The second design is based on the fundamental algorithms of calculating total numbers. It indicates that this study can operate it with the threshold value through a subtractor when the input is negative. On the contrary, an adder can be used when the information is positive. Based on the concept of logic optimization, this study chooses to use the only subtractors, and it just needs to focus on the borrow bit, which can indicate the more significant number. By connecting the MSB of the input with the subtractors through XOR gates, the selection can be achieved without using any multiplexer. In the process of removing and replacing the devices, it reached the optimization of the design. Then, this paper compared the minimum delay by calculating each stage’s size and finding that the second design is better. Finally, based on the dual design, this essay computed the energy consumption in the circuit and implement VDD optimization to obtain the minimum energy.

scholarly journals Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

2015 ◽  
Vol 25 (3) ◽  
pp. 319-331
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
New Formulation ◽  
Necessary And Sufficient ◽  
The Given

AbstractA new formulation of the minimum energy control problem for the positive 2D continuous-discrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.

scholarly journals A concise study on the expression of GFP protein in E. coli strain DH5α

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Maryada Garg ◽  
Anoop K. Dobriyal
Keyword(s):  
Protein Gene ◽  
Bacterial Culture ◽  
Research Work ◽  
Coli Strain ◽  
Foreign Gene ◽  
E Coli ◽  
Biotechnology Research ◽  
Indispensable Tool ◽  
The Given ◽  
Standard Grade

The GFP protein is a protein of high interest for molecular biologists and biotechnologists. Since 1994, this protein has proved to be an indispensable tool for molecular biology and biotechnology research work. This protein requires only oxygen and an energy source like glucose to work. It gives a green colour in presence of UV to blue light. This protein can be attached with the foreign gene to track its expression. The main aim of the task is to introduce GFP into the given bacterial culture. Induction of the protein gene is followed by Bradford assay; quantification of protein is done using this. The results of gene induction are checked via SDSPAGE and western blot. All preparations are of standard grade and all readings are taken in triplicates. A standard graph is also made to find out the protein in the unknown.

scholarly journals Landauer’s Principle of Minimum Energy Might Place Limits on the Detectability of Gravitons of Certain Mass

2021 ◽  
Vol 3 (6) ◽  
pp. 66-75
Author(s):  
Ioannis Haranas ◽  
Ioannis Gkigkitzis ◽  
Kristin Cobbett ◽  
Ryan Gauthier
Keyword(s):  
Minimum Energy ◽  
Cosmological Parameters ◽  
Heat Bath ◽  
Harmonic Oscillators ◽  
Thermal Bath ◽  
Graviton Mass ◽  
Exchange Information ◽  
Information Number ◽  
Landauer’S Principle ◽  
The Given

According to Landauer’s principle, the energy of a particle may be used to record or erase N number of information bits within the thermal bath. The maximum number of information N recorded by the particle in the heat bath is found to be inversely proportional to its temperature T. If at least one bit of information is transferred from the particle to the medium, then the particle might exchange information with the medium. Therefore for at least one bit of information, the limiting mass that can carry or transform information assuming a temperature T= 2.73 K is equal to m = 4.718´10-40 kg which is many orders of magnitude smaller that the masse of most of today’s elementary particles. Next, using the corresponding temperature of a graviton relic and assuming at least one bit of information the corresponding graviton mass is calculated and from that, a relation for the number of information N carried by a graviton as a function of the graviton mass mgr is derived. Furthermore, the range of information number contained in a graviton is also calculated for the given range of graviton mass as given by Nieto and Goldhaber, from which we find that the range of the graviton is inversely proportional to the information number N. Finally, treating the gravitons as harmonic oscillators in an enclosure of size R we derive the range of a graviton as a function of the cosmological parameters in the present era.

Calculations of electrostatic interactions in biological systems and in solutions

1984 ◽  
Vol 17 (3) ◽  
pp. 283-422 ◽  
Author(s):  
Arieh Warshel ◽  
Stephen T. Russell
Keyword(s):  
Electrostatic Interactions ◽  
Structural Information ◽  
Van Der Waals ◽  
Effective Radius ◽  
Biological Molecules ◽  
Electrostatic Energy ◽  
Energy Correlation ◽  
Polar Solvents ◽  
Charged Amino Acids ◽  
The Given

Correlating the structure and action of biological molecules requires knowledge of the corresponding relation between structure and energy. Probably the most important factors in such a structure– energy correlation are associated with electrostatic interactions. Thus the key requirement for quantative understanding of the action of biological molecules is the ability to correlate electrostatic interactions with structural information. To appreciate this point it is useful to compare the electrostatic energy of a charged amino acid in a polar solvent to the corresponding van der Waals energy. The electrostatic free energy, ΔGel, can be approximated (as will be shown in Section II) by the Born formula (ΔGel = –(166Q2/ā) (I – I/E)). Where ΔGel is given in kcal/mol, Qis the charge of the given group, in units of electron charge, āis the effective radius of the group, and E is the dielectric constant of the solvent. With an effective radius of charged amino acids of approximately 2 Å, Born's formula gives about – 80 kcal/mol for their energy in polar solvents where E is larger than 10. This energy is two orders of magnitude larger than the van der Waals interaction of such groups and their surroundings.

SCF-MO computational analysis of the geometric conformation and charge distribution in picric acid and alkali picrate salts

1996 ◽  
Vol 74 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Zbigniew Zimpel ◽  
Barbara R. Nelson ◽  
John A. Weil
Keyword(s):  
Charge Distribution ◽  
Computational Analysis ◽  
Picric Acid ◽  
Minimum Energy ◽  
Mulliken Charge ◽  
Resonance Effects ◽  
Molecular Electron ◽  
Optimized Model ◽  
Atomic Coordinates ◽  
Density Results

SCF-MO computations were employed in a study of picric acid, the –1 picrate ion, and Li, Na, and K picrates. Atomic coordinates from crystallographic structural analyses were used as initial parameters in the computation of the minimum-energy conformations of each free molecule at the 6-31G level. The Mulliken charge numbers for each atom in the optimized model molecules were calculated at the 6-31G** level. The induction and resonance effects of the OX group (X = H, Li, Na, K) on the trinitrophenyl ring are discussed. It is demonstrated that molecular (electron) isodensity surfaces (MIDCOs) describe charge-density results nicely compatible with the point Mulliken charge numbers. Key words: picrates, SCF-MO, charge distribution.

Electronic Structure and Bonding at the Al-terminated Al(111)/α-Al2O3(0001) Interface: A First Principles Study

2000 ◽  
Vol 654 ◽  
Author(s):  
Donald J. Siegel ◽  
Louis G. Hector ◽  
James B. Adams
Keyword(s):  
First Principles ◽  
Bond Order ◽  
Minimum Energy ◽  
Covalent Character ◽  
Population Analyses ◽  
Bonding Interaction ◽  
Optimized Model ◽  
Α Al2o3 ◽  
Mayer Bond Order ◽  
Atomic Coordinates

AbstractWe have performed ab initio calculations to determine the bonding character of the Al-terminated Al(111)/α-Al2O3(0001) interface. By using an optimized model in which all atomic coordinates were relaxed to their minimum energy positions, we have determined that Al-O bonds constitute the primary interfacial bonding interaction. Our electron localization, Mayer bond order, and Mul- liken population analyses reveal that these bonds are very similar to the cation-anion bonds found in the bulk oxide, and are therefore mainly ionic, with a smaller amount of covalent character. However, there is also evidence of metal-cation bonding across the interface, a result which could be significant to understanding bonding at interfaces with other corundum-like oxides.

Determination of minimum magnetic energy states in frozen plasmas

2003 ◽  
Vol 69 (5) ◽  
pp. 431-438
Author(s):  
C. A. PAOLA ◽  
A. M. PLATZECK
Keyword(s):  
Magnetic Energy ◽  
Energy State ◽  
Minimum Energy ◽  
Free Field ◽  
Initial State ◽  
Topological Constraints ◽  
Arbitrary Initial State ◽  
Nonlinear Force ◽  
The Given

As is known, the minimum magnetic energy state for a frozen plasma, subject to the infinite topological constraints, corresponds to a nonlinear force-free field. The magnetic flux invariance in ideal magnetohydrodynamics is possible in important astrophysical applications. We develop a method for explicitly obtaining a minimum energy state starting from an arbitrary initial state. This method does not require the explicit use of the invariance of the differential magnetic helicities. It is particularly useful when the minimum magnetic energy state for the given topological structure is unique. We show examples of the application of the method for this kind of system.

Crystal Structure of Cs2 [Pt(CN)4] · H2O

1977 ◽  
Vol 32 (2) ◽  
pp. 127-130 ◽  
Author(s):  
H. H. Otto ◽  
Heinz Schulz ◽  
K. H. Thiemann ◽  
H. Yersin ◽  
G. Gliemann
Keyword(s):  
Crystal Structure ◽  
Optical Emission ◽  
Water Molecules ◽  
X Ray Diffraction ◽  
X Ray ◽  
Square Planar ◽  
R Value ◽  
The Given ◽  
Emission Studies ◽  
Atomic Coordinates

The crystal structure of Cs2[Pt(CN)4] · H2O has been determined from X-ray diffraction data and refined to a conventional R value of 0.068 from 2210 reflections. The compound is hexagonal, α = 9.687(2) and c = 19.336(6) A, space group C62-P 61, Z = 6. The given atomic coordinates represent the absolute configuration. The nearly square planar Pt(CN)42- groups form a helix with respect to the c axis. The distance between neighbouring Pt atoms in the helix is 3.543(1) A. The normal of the Pt(CN)42- group is tilted about 15 deg to the c axis leading to a considerable overlap of metal orbitals which is suggested from optical emission studies. The protons of the water molecules form hydrogen bonds to nitrogen atoms of different helices. Both Cs atoms have similar sevenfold coordination.

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