Phasing diffuse scattering. Application of the<i>SIR2002</i>algorithm to the non-crystallographic phase problem

Carrozzini, Benedetta; Cascarano, G.; De, Liberato; Giacovazzo, Carmelo; Marchesini, Stefano; Chapman, Henry N.; He, Haifeng; Wu, Jin; Weierstall, Uwe; Spence, John C. H.

doi:10.1107/s0108767304012395

Cited by 6 publications

(2 citation statements)

References 19 publications

(24 reference statements)

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“…Since the diffraction pattern provides only |F ( Q)|, we need to obtain the associated phase before we can recover the molecular structure. There are iterative numerical algorithms that permit reconstructing the phase directly from the intensity data [17,18,[87][88][89][90][91][92][93][94][95][96][97][98][99][100][101]. These algorithms require intensity data sampled at twice the Nyquist frequency.…”

Section: B Phase-retrieval Algorithmmentioning

confidence: 99%

Computational studies of x-ray scattering from three-dimensionally-aligned asymmetric-top molecules

Pabst

Santra

2010

Phys. Rev. A

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We theoretically and numerically analyze x-ray scattering from asymmetric-top molecules three-dimensionally aligned using elliptically polarized laser light. A rigid-rotor model is assumed. The principal axes of the polarizability tensor are assumed to coincide with the principal axes of the moment of inertia tensor. Several symmetries in the Hamiltonian are identified and exploited to enhance the efficiency of solving the time-dependent Schrödinger equation for each rotational state initially populated in a thermal ensemble. Using a phase-retrieval algorithm, the feasibility of structure reconstruction from a quasiadiabatically aligned sample is illustrated for the organic molecule naphthalene. The spatial resolution achievable strongly depends on the laser parameters, the initial rotational temperature, and the x-ray pulse duration. We demonstrate that for a laser peak intensity of 5 TW/cm 2 , a laser pulse duration of 100 ps, a rotational temperature of 10 mK, and an x-ray pulse duration of 1 ps, the molecular structure may be probed at a resolution of 1Å. STEFAN PABST, PHAY J. HO, AND ROBIN SANTRA PHYSICAL REVIEW A 81, 043425 (2010)where the expansion coefficients [C(t)]The equation of motion for the expansion coefficients in the interaction picture (subscript I) readsIn the following, we assume we found [C L,I (t)] J 1 τ 1 M 1 J 0 τ 0 M 0 , the solution for the laser-only problem, i.e.,Ĥ rot +Ĥ L (t). Note that in the laser-only Hamiltonian no x-ray field is involved and we will drop the x-ray field indices in its solution.The interaction between the laser-aligned molecules and the x-ray field is taken into account by first-order perturbation theory. The solution of Eq. (7) becomesThe expectation values of interest can be calculated by043425-2 = − 1 2 2 J =0 J M=−J (−1) J +M [α pol ] [J ] L M U [J ] L −M (t), (18) | J τ M (t) has to be known to calculate the expectation values. However, | J τ M (t) can be written as a superposition of | J KM (t) [cf. Eq. (11)], and by using the same argument as for M, only | J KM (t) for K 0 are necessary to build all | J τ M (t) [cf. Eq. ( 13)]. This makes it attractive to propagate | J KM (t) rather than | J τ M (t) . Taking both symmetries together only the states | J KM (t) for 0 K,M J have to be propagated to understand the full system response, which can save up to a factor 4 in computational effort.The decoupling between even and odd K/τ states and M states also enhances efficiency and does not get destroyed by the presence of the interactionĤ L (t). Therefore, many [C L (t)] J τ M J KM remain zero throughout the alignment process. This holds for symmetric-top as good as for asymmetric-top rotors, since each |J τ M can be classified into the class E ± or O ± (cf. Sec. II A). The benefit is not just a speed-up by a factor 4; also the memory requirement to store [C L (t)] J τ M J KM , the matrixĤ L (t), and the matrices cos 2 θ lm is reduced by a factor 4. Memory size can become an issue on PCs when high J states are not negligible.

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Section: B Phase-retrieval Algorithmmentioning

confidence: 99%

Computational studies of x-ray scattering from three-dimensionally-aligned asymmetric-top molecules

Pabst

Santra

2010

Phys. Rev. A

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“…Four Rosetta-specific analyzers are implemented, including the Void Identification and Packing Analyzer (VIP) [14], Packstat [15], InterfaceAnalyzer [6], and LoopAnalyzer [6]. A user can also enable constraints for the pose and score function in the menu.…”

Section: Resultsmentioning

confidence: 99%

The PyRosetta Toolkit: A Graphical User Interface for the Rosetta Software Suite

Adolf-Bryfogle

Dunbrack

2013

PLoS ONE

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The Rosetta Molecular Modeling suite is a command-line-only collection of applications that enable high-resolution modeling and design of proteins and other molecules. Although extremely useful, Rosetta can be difficult to learn for scientists with little computational or programming experience. To that end, we have created a Graphical User Interface (GUI) for Rosetta, called the PyRosetta Toolkit, for creating and running protocols in Rosetta for common molecular modeling and protein design tasks and for analyzing the results of Rosetta calculations. The program is highly extensible so that developers can add new protocols and analysis tools to the PyRosetta Toolkit GUI.

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Lensless coherent imaging of proteins and supramolecular assemblies: Efficient phase retrieval by the charge flipping algorithm

Dumas¹,

Lee²,

Palatinus³

2013

Journal of Structural Biology

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Phasing diffuse scattering. Application of theSIR2002algorithm to the non-crystallographic phase problem

Cited by 6 publications

References 19 publications

Computational studies of x-ray scattering from three-dimensionally-aligned asymmetric-top molecules

Computational studies of x-ray scattering from three-dimensionally-aligned asymmetric-top molecules

The PyRosetta Toolkit: A Graphical User Interface for the Rosetta Software Suite

Lensless coherent imaging of proteins and supramolecular assemblies: Efficient phase retrieval by the charge flipping algorithm

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