<i>Classical Mechanics, 3rd ed.</i>

Goldstein, H.; Poole, Charles P.; Safko, John L.; Addison, Stephen R.

doi:10.1119/1.1484149

Cited by 1,724 publications

(2,609 citation statements)

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“…In general, the principal axes of each tensor in equation 1 need not be collinear. Euler rotations (29) were therefore used to express each tensor in a common reference frame, in this case the g-axis system of Co 2+ . The strategy used to diagonalize the energy matrix and simulate the field-swept powder EPR spectrum was described previously (30).…”

Section: Spectral Simulationsmentioning

confidence: 99%

Reaction of Adenosylcobalamin-Dependent Glutamate Mutase with 2-Thiolglutarate

et al. 2006

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We have investigated the reaction of glutamate mutase with the glutamate analog, 2-thiolglutarate. In the standard assay, 2-thiolglutarate behaves as a competitive inhibitor with K i = 0.05 mM. However, rather than simply binding inertly at the active site, 2-thiolglutarate elicits cobalt-carbon bond homolysis and the formation of 5′-deoxyadenosine. The enzyme exhibits a complicated EPR spectrum in the presence of 2-thiolglutarate that is markedly different from any previously observed with the enzyme. The spectrum was well simulated by assuming that it arises from electron-electron spin coupling between a thioglycolyl radical and low-spin Co 2+ in cob(II)alamin. Analysis of the zero-field splitting parameters obtained from the simulations places the organic radical at ∼ 10 Å from the cobalt, and at a tilt angle of ∼ 70° to the normal of the corrin ring. This orientation is in good agreement with that expected from the crystal structure of glutamate mutase complexed with substrate. 2-thiolglutarate appears to react in a manner analogous to glutamate by first forming a thioglutaryl radical at C-4 that then undergoes fragmentation to produce acrylate and the sulfurstablized thioglycolyl radical. The thioglycolyl radical accumulates on the enzyme suggesting it is too stable to undergo further steps in the mechanism at a detectable rate. Keywordsenzyme; coenzyme-B 12 ; free radicals; isomerization; substrate analog; EPR spectrometry Adenosylcobalamin 1 (Coenzyme B 12 , AdoCbl) is the coenzyme for a group of enzymes that catalyze unusual rearrangement or elimination reactions, as well as for class II ribonucleotide reductases. In these enzymes, the coenzyme serves as a masked form of the 5′-deoxyadenosyl radical that is generated through homolytic fission of the AdoCbl cobalt-carbon bond (1-6). An interesting and still poorly understood aspect of these reactions is how these enzymes catalyze homolysis of the coenzyme because the generation of free radicals from stable, closed shell molecules is energetically highly unfavorable.In all cases, homolysis of AdoCbl is tightly coupled to the formation of substrate-based radicals (or in the case of ribonucleotide reductase, a protein-based thiyl radical). The initially formed 5′-deoxyadenosyl radical is extremely unstable and has never been observed spectroscopically.

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Section: Spectral Simulationsmentioning

confidence: 99%

Reaction of Adenosylcobalamin-Dependent Glutamate Mutase with 2-Thiolglutarate

et al. 2006

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“…If holonomic, rheonomous constraints are imposed on a classical system of n atoms, and the D'Alembert's principle is assumed to hold, its motion is the solution of the following system of differential equations [17,28]:…”

Section: Calculation Of the Lagrange Multipliersmentioning

confidence: 99%

“…(2.6). Since (2.6) is a linear problem, one straightforward way to solve is to use traditional Gauss-Jordan elimination or LU factorization [17,36]. But these methods have a drawback: they scale with the cube of the size of the system.…”

Section: Numerical Calculationsmentioning

confidence: 99%

“…The essential ingredient in the calculation of the forces produced by the impo-sition of constraints are the so-called Lagrange multipliers [17], and their efficient numerical evaluation is therefore of the utmost importance. In this work, we show that the fact that many interesting biological molecules are esentially linear polymers allows to calculate the Lagrange multipliers in order N c operations (for a molecule where N c constraints are imposed) in an exact (up to machine precision), non-iterative way.…”

Section: Introductionmentioning

confidence: 99%

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Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

2011

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In order to accelerate molecular dynamics simulations, it is very common to impose holonomic constraints on their hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thus allowing, in principle, to reach longer total simulation times. The imposition of such constraints results in an aditional set of N c equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), that must be solved in one way or another at each time step of the dynamics. In this work it is shown that, due to the essentially linear structure of typical biological polymers, such as nucleic acids or proteins, the algebraic equations that need to be solved involve a matrix which is banded if the constraints are indexed in a clever way. This allows to obtain the Lagrange multipliers through a non-iterative procedure, which can be considered exact up to machine precision, and which takes O(N c ) operations, instead of the usual O(N 3 c ) for generic molecular systems. We develop the formalism, and describe the appropriate indexing for a number of model molecules and also for alkanes, proteins and DNA. Finally, we provide a numerical example of * Email: garcia.risueno@gmail.com the technique in a series of polyalanine peptides of different lengths using the AMBER molecular dynamics package.

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“…Among the major achievements of Sir Isaac Newton is the formulation of the Newton third law stating that any action is countered by a reaction of equal magnitude but opposite direction [1,2]. The total force in a system not affected by external forces is thus zero.…”

Section: Introductionmentioning

confidence: 99%

Retardation in Special Relativity and the Design of a Relativistic Motor

Yahalom

2017

Acta Phys. Pol. A

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The Newton third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is thus zero. However, according to the principles of relativity, a signal cannot propagate at speeds exceeding the speed of light. Thus the total force cannot be null at a given time. The above conclusion leads to the possibility of a relativistic engine in particular one that is based on a permanent magnet. The analysis is based on a previous paper in which we studied the relativistic effects in a system of two current conducting loops.

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Classical Mechanics, 3rd ed.

Cited by 1,724 publications

References 0 publications

Reaction of Adenosylcobalamin-Dependent Glutamate Mutase with 2-Thiolglutarate

Reaction of Adenosylcobalamin-Dependent Glutamate Mutase with 2-Thiolglutarate

Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

Retardation in Special Relativity and the Design of a Relativistic Motor

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