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Related Concept Videos

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
Polymer Classification: Crystallinity01:21

Polymer Classification: Crystallinity

Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...

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Related Experiment Video

Updated: May 22, 2026

Crystallization and In Situ Room Temperature Data Collection Using the Crystallization Facility at Harwell and Beamline VMXi, Diamond Light Source
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Published on: March 8, 2024

DNA, dichotomic classes and frame synchronization: a quasi-crystal framework.

Simone Giannerini1, Diego Luis Gonzalez, Rodolfo Rosa

  • 1Dipartimento di Scienze Statistiche, Università di Bologna, Via delle Belle Arti 41, 40126 Bologna, Italy. simone.giannerini@unibo.it

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 23, 2012
PubMed
Summary
This summary is machine-generated.

A new mathematical model reveals almost periodic structures in DNA and mRNA sequences, aiding in predicting protein synthesis reading frames. This discovery offers insights into biological information and protein synthesis efficiency.

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Mathematical Biology

Background:

  • Investigating the genetic code's properties is crucial for understanding protein synthesis.
  • The relationship between nucleic acid sequence organization and biological function requires further exploration.

Purpose of the Study:

  • To introduce a novel mathematical model of the genetic code.
  • To explore the almost periodic properties of DNA and mRNA protein-coding sequences.
  • To develop statistical classifiers for predicting the correct protein synthesis reading frame.

Main Methods:

  • Developed a new mathematical model of the genetic code, linking it to number and group theory.
  • Utilized dichotomic classes (binary variables) derived from the model.
  • Built statistical classifiers to predict the ribosome's reading frame.

Main Results:

  • Identified local informational structures in coding sequences related to frame synchronization.
  • Demonstrated short-range correlations and almost periodic structures in codon organization.
  • Found analogies between these structures and quasi-crystals.

Conclusions:

  • The mathematical model provides insights into the relationship between biological information and molecular shape in nucleic acids and proteins.
  • The developed tools offer potential for designing efficient algorithms for frame synchronization in protein synthesis.