European Molecular Biology Laboratory, c/o DESY, Notkestrasse 85, Hamburg, Germany.
J R Soc Interface. 2011 Jan 6;8(54):144-51. doi: 10.1098/rsif.2010.0297. Epub 2010 Aug 4.
Chirality is an important feature of three-dimensional objects and a key concept in chemistry, biology and many other disciplines. However, it has been difficult to quantify, largely owing to computational complications. Here we present a general chirality measure, called the chiral invariant (CI), which is applicable to any three-dimensional object containing a large amount of data. The CI distinguishes the hand of the object and quantifies the degree of its handedness. It is invariant to the translation, rotation and scale of the object, and tolerant to a modest amount of noise in the experimental data. The invariant is expressed in terms of moments and can be computed in almost no time. Because of its universality and computational efficiency, the CI is suitable for a wide range of pattern-recognition problems. We demonstrate its applicability to molecular atomic models and their electron density maps. We show that the occurrence of the conformations of the macromolecular polypeptide backbone is related to the value of the CI of the constituting peptide fragments. We also illustrate how the CI can be used to assess the quality of a crystallographic electron density map.
手性是三维物体的重要特征，也是化学、生物学和许多其他学科的关键概念。然而，由于计算上的复杂性，它一直难以量化。在这里，我们提出了一种通用的手性度量，称为手性不变量（CI），它适用于包含大量数据的任何三维物体。CI 区分了物体的手性，并量化了其手性的程度。它对物体的平移、旋转和比例不变，并且对实验数据中的适度噪声具有容忍性。不变量用矩表示，可以几乎瞬时计算。由于其普遍性和计算效率，CI 适用于广泛的模式识别问题。我们将其应用于分子原子模型及其电子密度图进行演示。我们表明，大分子多肽主链构象的出现与构成肽片段的 CI 值有关。我们还说明了如何使用 CI 来评估晶体学电子密度图的质量。
