Systematic Limitations in Concentration Analysis via Anomalous Small-Angle X-ray Scattering in the Small Structure Limit

Goerigk, G.; Lages, Sebastian; Huber, Klaus

doi:10.3390/polym8030085

Cited by 3 publications

(2 citation statements)

References 36 publications

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“…The full form of the ASAXS equation is quadratic in f ′( E ) due to a third purely resonant term: [ f ′( E ) v ( q )] 2 (see eq S2 ). 24 , 30 , 31 However, in our case the approximation in eq 1 is valid due to the relatively low magnitude of the purely resonant term as demonstrated by model ASAXS calculations and analysis of experimental data ( section S1 ). Here N / V represents the concentration of particles (Pro-SNAs in this case).…”

Section: Introductionmentioning

confidence: 78%

Defining the Structure of a Protein–Spherical Nucleic Acid Conjugate and Its Counterionic Cloud

et al. 2018

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Protein–spherical nucleic acid conjugates (Pro-SNAs) are an emerging class of bioconjugates that have properties defined by their protein cores and dense shell of oligonucleotides. They have been used as building blocks in DNA-driven crystal engineering strategies and show promise as agents that can cross cell membranes and affect both protein and DNA-mediated processes inside cells. However, ionic environments surrounding proteins can influence their activity and conformational stability, and functionalizing proteins with DNA substantively changes the surrounding ionic environment in a nonuniform manner. Techniques typically used to determine protein structure fail to capture such irregular ionic distributions. Here, we determine the counterion radial distribution profile surrounding Pro-SNAs dispersed in RbCl with 1 nm resolution through in situ anomalous small-angle X-ray scattering (ASAXS) and classical density functional theory (DFT). SAXS analysis also reveals the radial extension of the DNA and the linker used to covalently attach the DNA to the protein surface. At the experimental salt concentration of 50 mM RbCl, Rb+ cations compensate ∼90% of the negative charge due to the DNA and linker. Above 75 mM, DFT calculations predict overcompensation of the DNA charge by Rb+. This study suggests a method for exploring Pro-SNA structure and function in different environments through predictions of ionic cloud densities as a function of salt concentration, DNA grafting density, and length. Overall, our study demonstrates that solution X-ray scattering combined with DFT can discern counterionic distribution and submolecular features of highly charged, complex nanoparticle constructs such as Pro-SNAs and related nucleic acid conjugate materials.

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Section: Introductionmentioning

confidence: 78%

Defining the Structure of a Protein–Spherical Nucleic Acid Conjugate and Its Counterionic Cloud

et al. 2018

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“…Anomalous dispersion corrections typical for ASAXS experiments of three-phase systems performed in the energy range of L III -absorption edges using the energy of the absorption edge. Pb serves as an example [30]. …”

Section: Appendix 2: Details Of the Mathematical Algorithm Employed Imentioning

confidence: 99%

The Significance of Solutions Obtained from Ill-Posed Systems of Linear Equations Constituted by Synchrotron Radiation Based Anomalous Small-Angle X-Ray Scattering

Goerigk¹

2018

ALAMT

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Synchrotron radiation based experimental techniques known as Anomalous Small-Angle X-ray Scattering (ASAXS) provide deep insight into the nanostructure of uncountable material systems in condensed matter research i.e. solid state physics, chemistry, engineering and life sciences thereby rendering the origin of the macroscopic functionalization of the various materials via correlation to its structural architecture on a nanometer length scale. The techniques constitute a system of linear equations, which can be treated by matrix theory. The study aims to analyze the significance of the solutions of the stated matrix equations by use of the so-called condition numbers first introduced by A. Turing, J. von Neumann and H. Goldstine. Special attention was given for the comparison with direct methods i.e. the Gaussian elimination method. The mathematical roots of ill-posed ASAXS equations preventing matrix inversion have been identified. In the framework of the theory of von Neumann and Goldstine the inversion of certain matrices constituted by ASAXS gradually becomes impossible caused by non-definiteness. In Turing's theory which starts from more general prerequisites, the principal minors of the same matrices approach singularity thereby imposing large errors on inversion. In conclusion both theories recommend for extremely ill-posed ASAXS problems avoiding inversion and the use of direct methods for instance Gaussian elimination.

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Anomalous small-angle X-ray scattering for materials chemistry

Sun

2021

Trends in Chemistry

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Systematic Limitations in Concentration Analysis via Anomalous Small-Angle X-ray Scattering in the Small Structure Limit

Cited by 3 publications

References 36 publications

Defining the Structure of a Protein–Spherical Nucleic Acid Conjugate and Its Counterionic Cloud

Defining the Structure of a Protein–Spherical Nucleic Acid Conjugate and Its Counterionic Cloud

The Significance of Solutions Obtained from Ill-Posed Systems of Linear Equations Constituted by Synchrotron Radiation Based Anomalous Small-Angle X-Ray Scattering

Anomalous small-angle X-ray scattering for materials chemistry

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