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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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The phase problem for two-dimensional crystals. I. Theory.

Romain D Arnal1, Rick P Millane1

  • 1Computational Imaging Group, Department of Electrical and Computer Engineering, University of Canterbury, Christchurch, New Zealand.

Acta Crystallographica. Section A, Foundations and Advances
|October 27, 2017
PubMed
Summary
This summary is machine-generated.

Determining protein structures from 2D crystals is feasible with new X-ray sources. Molecular envelope data significantly narrows down potential solutions, enabling unique structure determination.

Keywords:
XFELsab initio phasingphase problemtwo-dimensional crystals

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Area of Science:

  • Structural biology
  • Crystallography
  • Biophysics

Background:

  • The phase problem is a critical challenge in crystallography.
  • New X-ray free-electron laser (XFEL) sources enable diffraction from 2D crystals for protein structure determination.
  • Conventional 3D crystallography faces limitations in certain applications.

Purpose of the Study:

  • To analyze the phase problem specific to 2D crystal diffraction.
  • To assess the feasibility and challenges of protein structure determination using 2D crystals.
  • To evaluate methods for resolving phase ambiguity in 2D crystallography.

Main Methods:

  • Theoretical analysis of the phase problem in 2D crystallography.
  • Investigation of molecular envelope information's impact on phase determination.
  • Assessment of molecular surface features and data completeness effects.
  • Simulations of phase retrieval for 2D crystal data (as described in a companion paper).

Main Results:

  • The phase problem for 2D crystals is more constrained than for 3D crystals.
  • A large number of solutions persist without prior information.
  • Molecular envelope data effectively reduces the solution space.
  • Unique solutions are achievable with sufficiently distinct molecular envelopes.

Conclusions:

  • Protein structure determination from 2D crystals is a promising approach with XFELs.
  • Molecular envelope information is crucial for resolving phase ambiguity.
  • Further investigation into surface features and data completeness is needed for ab initio phasing.