Quantitative evaluation of the near-C2 symmetry of the bacterial photosynthetic reaction center

Keinan, Shahar; Pinsky, Mark; Plato, M.; Edelstein, Josef; Avnir, David

doi:10.1016/s0009-2614(98)01203-2

Cited by 10 publications

(14 citation statements)

References 27 publications

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“…The continuous symmetry measure (CSM) methodology33–54 will be used in this article, because it is simple and versatile. The CSM is the normalized distance between the original structure and the closest symmetrical object.…”

Section: Introductionmentioning

confidence: 99%

“…If the original structure is symmetric, the measure is zero and as the structure becomes more distorted and less symmetric, the value of the measure increases. Since the introduction of the method, it proved in several publications to provide quantitative correlations between symmetry and various physical properties 34–49. Analytical procedures for calculating the CSM and finding the position of the symmetry elements were recently published, making the calculations more accurate than before 50.…”

Section: Introductionmentioning

confidence: 99%

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Quantitative symmetry and chirality—A fast computational algorithm for large structures: Proteins, macromolecules, nanotubes, and unit cells

2011

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Symmetry is one of the most fundamental properties of nature and is used to understand and investigate physical properties. Classically, symmetry is treated as a binary qualitative property, although other physical properties are quantitative. Using the continuous symmetry measure (CSM) methodology one can quantify symmetry and correlate it quantitatively to physical, chemical, and biological properties. The exact analytical procedures for calculating the CSM are computationally expensive and the calculation time grows rapidly as the structure contains more atoms. In this article, we present a new method for calculating the CSM and the related continuous chirality measure (CCM) for large systems. The new method is much faster than the full analytical procedures and it reduces the calculation time dependency from N! to N(2), where N is the number of atoms in the structure. We evaluate the cost of the applied approximations, estimate the error of the method, and show that deviations from the analytical solutions are within an error of 2%, and in many cases even less. The method is applicable at the moment for the cyclic symmetry point groups- C(i), C(s), C(n), and S(n), and therefore it can be used also for chirality measures, which are the minimal of the S(n) measures. We demonstrate the application of the method for large structures across chemistry: proteins, macromolecules, nanotubes, and large unit cells of crystals.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantitative symmetry and chirality—A fast computational algorithm for large structures: Proteins, macromolecules, nanotubes, and unit cells

2011

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“…size of the structure. We have used this function intensively for the estimation of symmetry and chirality content, where in that case N k are the vertices coordinates of a searched nearest reference shape that has the desired symmetry or achirality, respectively 6, 7. Here, however, we use S 0 as a general distance function between any definitions of P k and N k .…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of the estimation of distance measures

2003

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Distance functions serve for quantitative evaluation of the degree of similarity, shape content, symmetry, chirality, and so on. We have developed a general methodology and a general computational tool for the estimation of the value of the distance function and of the error in that estimation, which originates in the experimental uncertainty in the location of the set of points of the studied structure (such as that expressed by the atomic displacement factor in X-ray data analysis).

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“…CSM and CCM analyses have been applied successfully to a variety of symmetry and chirality problems in chemistry. 9,10 It should be noted that the study of the distance from reflection symmetry and from achirality are distinctly different issues that may, but need not, coincide. Both measures are valuable and may cater to different applications.…”

Section: Introduction Lthough Symmetry Serves As a Central Tool Inmentioning

confidence: 99%

“…Examples we analyzed recently, using the CSM approach, include the near C symmetry of the photosynthetic reaction 2 center and that of the HIV-protease. 10 We begin with a general discussion of procedures for the calculation of the closest achiral object, using solutions to the pose estimation problem; that is, finding the best superpositioning of 11 ᎐ 13 Ž two sets of points.…”

Section: Introduction Lthough Symmetry Serves As a Central Tool Inmentioning

confidence: 99%

Continuous symmetry measures: Finding the closest C2-symmetric object or closest reflection-symmetric object using unit quaternions

Salomon¹,

Avnir²

1999

J. Comput. Chem.

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A closed‐form solution is provided for the problem of finding the closest reflection‐symmetric object, and its relation to the problems of finding the closest achiral object, the closest inversion‐symmetric object, and the closest projection plane is discussed. The key to the solution is reducing this problem to the problem of finding the best (least squares) c2 rotation between two sets of points, in addition to solving the problem of finding the closest C2‐symmetric object. The solution is derived using the quaternion representation of rotation. It is shown that calculation of the best c2 rotation can be reduced to the diagonalization of the outer product matrix of the pair (between the two sets). ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 772–780, 1999

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Quantitative evaluation of the near-C2 symmetry of the bacterial photosynthetic reaction center

Cited by 10 publications

References 27 publications

Quantitative symmetry and chirality—A fast computational algorithm for large structures: Proteins, macromolecules, nanotubes, and unit cells

Quantitative symmetry and chirality—A fast computational algorithm for large structures: Proteins, macromolecules, nanotubes, and unit cells

Statistical analysis of the estimation of distance measures

Continuous symmetry measures: Finding the closest C2-symmetric object or closest reflection-symmetric object using unit quaternions

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