A new least-squares refinement technique based on the fast Fourier transform algorithm

Agarwal, R.

doi:10.1107/s0567739478001618

Cited by 242 publications

(184 citation statements)

References 9 publications

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“…One way that is widely used in X-ray crystallography to compute the electron density around an atom is via the analytic Fourier transform of the atomic scattering factor. 84,85 Conventionally, the atomic scattering factor was fitted with the sum of some Gaussian terms (with a and b are tabulated constants for each atom, we use here the sum of six Gaussians by Su and Coppens 86 ),…”

Section: Direct Calculationmentioning

confidence: 99%

Extracting water and ion distributions from solution x-ray scattering experiments

Nguyên

Pabit

Pollack

et al. 2016

The Journal of Chemical Physics

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Small-angle X-ray scattering measurements can provide valuable information about the solvent environment around biomolecules, but it can be difficult to extract solvent-specific information from observed intensity profiles. Intensities are proportional to the square of scattering amplitudes, which are complex quantities. Amplitudes in the forward direction are real, and the contribution from a solute of known structure (and from the waters it excludes) can be estimated from theory; hence, the amplitude arising from the solvent environment can be computed by difference. We have found that this "square root subtraction scheme" can be extended to non-zero q values, out to 0.1 Å −1 for the systems considered here, since the phases arising from the solute and from the water environment are nearly identical in this angle range. This allows us to extract aspects of the water and ion distributions (beyond their total numbers), by combining experimental data for the complete system with calculations for the solutes. We use this approach to test molecular dynamics and integral-equation (3D-RISM (three-dimensional reference interaction site model)) models for solvent structure around myoglobin, lysozyme, and a 25 base-pair duplex DNA. Comparisons can be made both in Fourier space and in terms of the distribution of interatomic distances in real space. Generally, computed solvent distributions arising from the MD simulations fit experimental data better than those from 3D-RISM, even though the total small-angle X-ray scattering patterns are very similar; this illustrates the potential power of this sort of analysis to guide the development of computational models. Published by AIP Publishing. [http://dx

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Section: Direct Calculationmentioning

confidence: 99%

Extracting water and ion distributions from solution x-ray scattering experiments

Nguyên

Pabit

Pollack

et al. 2016

The Journal of Chemical Physics

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“…Total coordinates (protein and water) were extracted at 100-ps intervals (100 coordinate sets total/simulation) and were aligned by performing a least-squares fit on the protein Ca atoms. The total electron density of all aligned frames was determined by calculating crystallographic structure factors followed by a Fourier transform using the programs SFall [20] and FFT [21] respectively of the CCP4 software suite [22]. The electron densities were calculated with the protein and water in a P1 unit cell equivalent to the box size used for the MD simulation.…”

Section: Molecular Dynamics Simulationsmentioning

confidence: 99%

Engineering a naturally inactive isoform of type III antifreeze protein into one that can stop the growth of ice

et al. 2012

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a b s t r a c tType III antifreeze proteins (AFPs) can be sub-divided into three classes of isoforms. SP and QAE2 isoforms can slow, but not stop, the growth of ice crystals by binding to pyramidal ice planes. The other class (QAE1) binds both pyramidal and primary prism planes and is able to halt the growth of ice. Here we describe the conversion of a QAE2 isoform into a fully-active QAE1-like isoform by changing four surface-exposed residues to develop a primary prism plane binding site. Molecular dynamics analyses suggest that the basis for gain in antifreeze activity is the formation of ice-like waters on the mutated protein surface.

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“…As used for Poisson-Boltzmann electrostatics calculations in [22], a characteristic function f (x) is selected to represent an 'inflated' van der Waals-based accessibility (1) where (x i , r i ) are the centers and radii of the N atoms in the biomolecule, and σ is the radius of the diffusing species, here we choose σ = 2 [43]. When σ = 0, the VWS is constructed.…”

Section: Gaussian Density Mapmentioning

confidence: 99%

Quality meshing of implicit solvation models of biomolecular structures

Zhang

Bajaj

2006

Computer Aided Geometric Design

104

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This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gaussian isotropic kernel functions and a two-level clustering technique. This enables the selection of a smooth implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flow techniques are used to improve the surface and volume mesh quality. Several examples are presented, including generated meshes for biomolecules that have been successfully used in finite element simulations involving solvation energetics and binding rate constants.

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A new least-squares refinement technique based on the fast Fourier transform algorithm

Cited by 242 publications

References 9 publications

Extracting water and ion distributions from solution x-ray scattering experiments

Extracting water and ion distributions from solution x-ray scattering experiments

Engineering a naturally inactive isoform of type III antifreeze protein into one that can stop the growth of ice

Quality meshing of implicit solvation models of biomolecular structures

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